I'll be brief, as I think your sitaution is pretty clear. My advice to you would be:
1. Assume he had a physical affair.
2. Assume he's remorseful now, and wants to make it right and work on the marriage.
3. Tell him what you would need, in terms of no-contact, transparency, marriage counseling, etc., to go forward and try.
If you can't forgive the adultery, you certainly have every right to end the marriage, but I don't sense that that's what you want to do and he doesn't seem to want that either. You're both going to have to sacrifice something here -- you're going to have to try to forgive his infidelity, and be OPEN with him if he chooses to tell you about it, and he's going to have to agree to your list of terms (including MCing).
