Ivehearditallnow refreshingly candid description - except that pigs are supposedly very intelligent animals.
Op - there must be NO CONTACT - otherwise your husband's head is still wedged firmly up his nether end. I don't give a tinker's cuss for the feelings of the ow - what did she think was going to happen? Anyway, she hardly needs comfort from a man in such a .. position. These things are tediously predictable. Your needs, op, as an entirely innocent party, are FAR more pressing.
No one can or should tell you whether you should go or stay, but seriously do not let him stuff himself with cake, you will have to take away the supply at your end. A visit to a lawyer (free half hour consultation) is bracing and will remind you that you too have rights - to live with another adult if nothing else. You do not have to follow through. I did this, and haven't needed to pursue a divorce (at this date, ha) but I secured the best family law firm in the county and it made me feel safer and more confident that if the worst happened, I would be OK. And our dcs too.
There is really nothing you can do if he won't stop, you cannot control another person. But you can decide on your own actions and what you will tolerate. No contact is the absolute minimum. But cheaters lie, as you're seeing now, and you cannot police him forever. It may the toughest situation you've ever had to face, I really feel for you. Surround yourself with good friends, time to weed out anyone toxic. Ask for support.
And remember this is NOT YOUR FAULT, these are his choices. Affairs are highly addictive and make idiots of the participants. You're a bystander and though it feels like shit atm, you still have your wits about you.
There is a thing called the 180 - here's a post: beingabeautifulmess.wordpress.com/the-180/
I like where she says: 'It’s about not getting sucked into unnecessary drama.' Exhausting for you to have to put up with this nonsense. I don't know what people think of the 180, mumsnetters might believe it's manipulative or demeaning or that black bin liners full of his clothes on the front lawn and a change of locks is a better bet. You certainly have every right to be extremely angry op. There is no justification for him treating you in this way. At the very least, he has to STOP LYING.
Good luck :)