Denial & minimising are just the next steps. You'll hear all about how lonely he felt, how preoccupied you were or whatever - it'll be down to YOU not meeting his needs blah blah.
If it's not physical I'll eat my socks. Sorry, but it's just all part of the 'only admit to what you know she knows.
In itself it's irrelevant really, however, whilst he's still lying to you there's NO WAY you can make it work.
It seldom works after an affair, unless it's just the (usually) betrayed woman sucking it up. Very occasionally couples me through it feeling stronger & happier, but ONLY if there is GENUINE remorse & understanding that it's solely the 'fault' of the person that cheated. Yes the marriage might have been breaking down, yes the other person might have contributed to that, but the affair s ONLY diwn to the oerson that had it. End of. Until the cheat gets to that pkace in their own head and stops blaming their partner, it's not possible to make the marriage a happy one again.
I tried, I really, really tried - but it was pre MN & I didn't understand so much that I do now. I'd never put myself through that again, it's hell on earth, it really is. No matter how much you love hm, no matter how much you want to trust him you'll turn yourself inside out worrying when he's on his phone, working away, running late, moody etc. I'm not trying to upset you, but I wish to hell I'd understood this before I accepted his tears & pleading to 'make it work' - which basically meant accepting it had happened but it was all over now, that 'they' would just be friends (over my fucking dead body) and the stupid fuck actually said one day 'I don't want to talk about it anymore, I just want to 'put it to bed'. Well, let's just say it's a phrase he's probably never uttered since.
You know he's still lying. I'd tell him to pack a bag and go. Don't be afraid to tell people the truth. I understand it feels humiliating, it shoukdnt, but it does. However, the sooner we all stop blaming ourselves for our partners having affairs & stop feeling that it's us that's inadequate the better and the best way to do this is fake it until you make. Tell people he's a stupid weak man who had an affair & now appreciates what he's just lost.
Be strong. You can do this.
If he's genuinely remorseful & genuinely wants to rebuild your marriage you can still do that, but you need him to move out first. It's hard, I know, you just want to cling ont what you have left & not risk it, but you really, really can't if you want it to work.