The traits that allow someone to be a cheat, low self esteem, inability to self soothe, selfishness, the need for validation (smoke up the arse), people pleasing tendencies, the need to be a good guy, the ability to lie and compartmentalise etc are sadly not the traits needed to be good at recovering from an affair (emotional or physical).
To recover he will have to realise what traits he has that allowed him to have a ‘but’ in his fidelity. I am faithful but not if my wife is not watching. I am faithful but it doesn’t count unless it’s sex. I am faithful but not if I’m going through a hard time.
He didn’t confess he was caught. Did he know the husband knew? Have they discussed (the woman and him).
You cannot make another human cheat, you also cannot make them be faithful. Two people in the same situation - one may cheat the other may not. You did not cause this and your personality may mean you cannot ‘fix’ this. Your need for loyalty, honesty and fidelity has not been met- you could in theory use this to justify cheating. But how would that help you or your marriage. Shagging your loyal and honest postman (never steals your post and is always on time) won’t help your marriage in any way at all.
Cheaters cheat as they have personality traits that say cheating is okay in certain circumstances. We all have the ability to cheat, I could sign up on tinder this minute and no doubt have some validation by lunchtime. So I think it’s easier to say why don’t I cheat on my husband. It has nothing to do with him at all - I don’t cheat for me. I made vows willingly in front of friends and family. I said I’d be faithful and honest and I want to like the woman I see in the mirror each morning. So I am faithful for me. Not him, he’s annoying at times, if I am faithful for him then I could easily justify being unfaithful (if he annoys me or we argue for example). I am faithful for me. I like me. I like my choices. So I’m faithful for me and he is the collateral damage to my choices. My word means something to me and I want to be someone who keeps my word. So I do - for me.
Can you recover? Build something new? Maybe. But his personality traits, that need for validation, maybe avoiding confrontation (he didn’t tell you), his ability to lie - are not traits that will find your anguish and pain easy. You won’t be able to validate and soothe him - then what happens? Your honesty will make him uncomfy - then what happens? You may find you eventually see his traits in another way. You had empathy for his struggles but you may now start to look at him as being needy and pathetic. His desire for smoke up his butt is unattractive and you will see it in a neon light going forward and it will be a reminder of what he does to get an ego boost. It will be tough and that’s without you dissecting what a marriage means to you and do you still have enough to want to keep this one.
Good luck op. No judgement here either way. He’s pathetic for putting you in this position. Good luck.