This sounds so familiar to me. Except for me it's no mystery who the confidant is (I don't know if it's better to know or not...). At any rate, I asked H to consider counseling, despite his protestations simply because I wasn't sure where else we could go from here by ourselves. I told him straight up, "I don't know what else to do." He has reluctantly agreed to "give it a shot," and we have our first appt tomorrow. I think part of his reluctance was that he was afraid the counselor would make it all out to be his fault. When I talked to her on the phone to make our appt, I relayed that and she said the relationship is her client, not me or him, so she works to serve the relationship and not choose sides - that seemed to make him feel a lot better. Maybe that's part of what your H is worried about?
I also agree with BaBa about asking what he suggests instead - I did the same thing, and all I got was a shrug.

I think when he realized he had no other ideas, either, counseling maybe didn't seem so bad.
Good luck! And I think you should maybe look into going just for yourself, even if he won't go with you. At least you'd have someone to talk things over with impartially. Someone gave me some great advice on one of my threads: you can only be in charge of what YOU do; how he acts is up to him. (I'm paraphrasing.) (((HUGS)))