So take him up on the counseling. If he is serious then he will cut all contact with OW. That may even involve changing phone numbers and email addresses. Make him show you some action before you let him come back. You can not work on it with a third person involved.
100% no-contact -- forever -- via a little OK'd and mailed by YOU, plus full transparency. Tell him that the marriage may take months, or even a couple of YEARS to fix, but that the DECISION, if he's serious, should only take five minutes.
Then start counting.
Or, if you're feeling generous, give him 24 hours, but tell him not to bother coming back over or to say ANY more "I've changed my mind" talk until he's ready to agree to this. Assure him that once he's ended it with OW, and the two of you begin to work thru the infidelity pain, that you are ready to address ANY and ALL issues in the marriage, but since he is the one who broke his wedding vows, this (the adultery) has to come first.
