OP: a few posters are questioning why your husband has decided to come clean now, specifically. Your own posting history answers that question very clearly. He's sensed a sea change in your attitude. He had you on the hop, questioning yourself, blaming yourself for every negative nuance happening in your relationship, in the end resulting in your undertaking counselling. His gaslighting was, in short, successful - as it often is before the scales fall from our eyes and we realise what's happening. The good news is that once that realisation happens, they can't take us in in the same way again.
Of late, you've realised the issue is him, not you, and found it liberating. When he's continued with the line of what an appalling person he is, you've laughed in his face. Bet he wasn't expecting that. These abusive men - and please be in no doubt that he is one of them - sense these changes in attitude as surely as if we are sending them radio signals. He's noticed a renewed strength in you; a refusal to accept yourself as the bad person, and likely, too, a sense of distance as you prepare to extract yourself from the situation. He now sees his cosy domestic situation has come under threat and, despite his promises to OW, he doesn't want that to happen as it will create trouble and inconvenience for him.
This is not a man who loves you. His manipulation is breathtaking: in withholding affection from you to make you desperate and then bestowing it only when he wants to bring you back into line and maintain the status quo precisely as it is. This is truly loathesome behaviour. Likewise the suicide threats. These are also recognised patterns of abuse: the cycle goes from love-bombing to devaluing and, eventually, discarding.
Your instincts are rock solid. You intended to keep your knowledge of his affair to yourself because you knew precisely how we would work on you: and he has proved you right. You recognised The Script. The above cycle of love-bombing to 'discard' is another variation on the script. The cycle will repeat itself. This will continue happening, ad nauseam, for as long as you stay. Trust yourself, OP. You were right - about all of it - so far. You're also right that this will be your life if you stay. Cut to that part right now, and you'll save yourself a whole world of grief. There is no future to be had - none - with a personality like this unless you sacrifice everything of yourself in the process, ending up as a hollowed-out shell.
I'm sorry that you too have found yourself embroiled in a relationship with such a destructive man. Final point: he won't change. They never do. 