So. Your husband is cheating on you. *

*Derived from hundreds of real life cases.

You must be feeling very awful and probably are swimming in a pool of helplessness feelings. I really feel for you. 
Look at what you have learned. You are here so you must have proven already within the realm of "balance of probability" that your husband is having an extramarital affair in its incipient stage. (It really sounds quite immature.) In Civil / Family law, you do not have to prove this "beyond a doubt". That you are unhappy with the facts of his behaviour is sufficient for you to take remedial action.

If you have decided that is the case for certain, I want to get you focused on some next best steps considering you already know plenty and don't need to learn much more about your spouse's frivolity. And that's what it is: frivolous. And of course, a significant betrayal. And that hurts.

Don't despair. You can take charge of your situation; bring some personal control to the matter; and arrive at a satisfactory repair of your marriage. You know what the alternatives are so I will focus on helping you construct a plan to bring wellness back into your marriage. i.e..: fix your problem and prevent its recurrence. This is personal advice only. For legal advice, see your lawyer. Read on. 

Before getting into the plan, I am concerned about one aspect of self-help sleuthing. 
In most states and provinces watching and besetting another person is a criminal offence in the misdemeanor/summary offence category. It has good reason; avoiding a breach of the peace -- avoiding family violence in other words. The law tends to frown on people doing their own matrimonial sleuthing inasmuch as it would include surveillance. The reason for this is that motivation is already present and if a confrontation erupts (which in family matters is statistically inevitable) there is the makings of a premeditated violent crime. The law seeks to prevent its occurrence and deals with incipiency very harshly. Solution: Do all the digging and legwork you want but get a professional person in your local area to do your actual tailing and surveillance if needed. 
So now that we are past that word of caution, I would say "yes", you have a problem; and "yes" you can improve or fix it. 

It is so often stated this way. The straying spouse claims to want to stay in the marriage and had no intention of leaving it but got "tangled up" somehow. If you believe your spouse loves you and has some commitment to staying within the bounds of marriage and further, seems to know the rules and has told you he has made a conscious decision to "not go outside the marriage", then look at the positive. Too often the problem is some life-passage-related quirks for which a vent has been found. 

Think of this. Dieing really sucks. Facing that reality while still very much alive can cause some fairly extreme behaviour. Seemingly without reason. The victim hasn't a clue why he/she behaves that way. (Seems that men get it BAD.) The fleeting glimpse of the obvious one comes face to face with at some point in mid-life, the facing of immortality causes some people's ID and Ego to go berserk in search for youthfulness. There is a grave risk that the aftermath of a mid-life crisis sees one with nothing of the true assets built up in the first half of life. It can otherwise be a good thing. Certainly, above all, a person suffering a mid-life crisis can be extremely vulnerable. 

All humans are weak and those weaknesses have focus points that some persons have an uncanny knack for detecting and focusing on, when in conquest, say for example, when a woman has decided to target a male who is married. There are lots of social anthropological studies (results filed at many universities web sites) done in this area. Search if you would like to understand this better thru google, Lycos or whatever. 

Looking at your spouse and correspondent, you are dealing with two people who are now stepping outside the bounds of 'niceness'; past playing by the rules. Your spouse  is being very foolish and irresponsible etc. 

If you have decided you want to bring your spouse back into a properly constituted matrimonial framework, then you must have no concern about his correspondent. None whatsoever. Forget her. As he must, you must as well. He must break his connections with this person. (A family counselor can explain how this is done under your circumstances. The counselor would need to mediate a resolution.)

Believe What You Know

When a spouse has a secret affair, they develop deviant, dishonest, sneaky skills. You would hardly believe you knew this person if you knew it all: the games that are played to avoid detection.

Don't argue the affair with your spouse.  Your spouse has been deceiving you and is lying to you about the matter and you can't know what is and what isn't truthful among the things he tells you. There is very little point in you discussing anything of this matter with him. Why would you continue to negotiate or arbitrate on your own with a person who has already established a set of ground rules that has untruthfulness as a basis? Your mode is now action oriented and you need some outside assistance. 

Don't accept "We are just friends."  That you are unhappy with the facts of his behaviour is sufficient for you to take remedial action. The alleged platonic relationship is apparently not platonic. Trust your senses. It has become immaturely intimate. 

You are not completely powerless.  Your spouse, insofar as civil law is concerned, is liable to your action under the various matrimonial statutes where adultery is an issue of law.

Betrayal is the most important issue. 
 You need to ask yourself what you want to do about the fact that your spouse is carrying on outside the marriage. Ask yourself, on the evidence, is this just a fairly frivolous affair and not a deep emotional thing? Are you prepared to vacate the marriage? I would guess that you don't know what you want to do. Further, marriages usually survive affairs if there is no significant emotional betrayal. Otherwise they don't, quite honestly. I am sure you are not quite ready to accept that statement right now, because surely you are very angry. But make these thoughts the underlying root for hope and some positive solution-oriented action. 
If you are concluding the above as I am then you need to find solutions that will return happiness and wellness to the matrimonial relationship; 'rehabilitate', your spouse who seems to be living in a false paradigm; and give him a new set of rules and understandings as well as proactive ingredients for making a marriage and a family work properly. 

Action Oriented Solutions In Four Key Steps

1. It's time to build a help group or SUPPORT TEAM FOR YOU. Consult with your lawyer and your family doctor as well as family members and so on. Build a support team. Be truthful; take the high road; do not lie or exaggerate to any persons who are members of your support team. Remember: DON'T BRING THE FIGHT TO THESE PEOPLE, BRING YOUR QUEST FOR ADVICE AND SOLUTIONS. Illicit their support. Try not to be acrimonious in the face of other people. If you need to "dump" some emotions, see a councilor for yourself, on your own. That's where you can best take your hard feelings and lay them out and deal with them.  And of course, a close family member, Aunt, Mom whoever; anyone you may find to be helpful and supportive.
   
2. Locate on your own what you think would be an acceptable source for family/marriage counseling. Check it out, meet the councilor alone and generally make sure you find what YOU want and a rapport that suits your self. 
   
3. Having located a good marriage councilor that you like, make arrangements to see this person together with your spouse on short notice. 
   
4. Confront your spouse. Inform him what you know as in the aforementioned four points on credibility and as follows: 

   a) You know he is lying to you about the matter and you don't know what is and what isn't truthful among the things he tells you so you refuse to accept any further explanations or excuses.
   
   b) The alleged platonic relationship is not platonic; it has become intimate. 
   
   c) Your husband, insofar as civil law is concerned, is liable to your action under the various matrimonial statutes where adultery is an issue of law. 
   
   d) His betrayal of you is the most important issue. And...
   
   e) You insist on immediate cessation of the illicit relationship [no further contact] and immediate attendance before a marriage councilor with a view to creating an extensive remedial plan, long term, for his rehabilitation and the re-constitution of the marriage. 

5. 
   Avoid argument over any of the issues with your spouse. You know what you know so why bother. The perpetrator will lie to you and talk you round in circles -- feed you lines that have been planted in his head with his own forethought and from his correspondent. You set out what you want, remain steadfast, and focus on your goal which is to fix your problem. If he refuses - go to your lawyer. Your lawyer can perhaps frame a letter as a notice that you intend to seek family-law remedies (separation, divorce and even punitive civil litigation) if he chooses not comply with your request. That is not an improper threat but the correct establishment of your position in the matter. 
6. Stay in touch with your support group.
   

 Micheal J. O'Brien

Good Luck!