I'm very sorry he chose to destroy your marriage. Obviously, it won't be the first time - what are the odds he'd get caught the very first time - and even if by some miracle it was the first time he'd betrayed you, nothing he said can ever be trusted again.
As he is a liar who stuck his penis into another woman, his version of events should never be believed.
He is a liar. This is who he is. You are living with a liar who sticks his penis in willing women. This is your reality and this will not change. You will live day upon day with this distress and you will never forget. Every time he touches you, you will wonder what he has been up to and will visualise him fucking someone else. Every memory of every time he went away without you or was somewhere he could have cheated will be examined. His declarations of love, every good memory, all tainted now.
After a while, he will start kicking up a fuss and saying how unreasonable and cruel you are being still going on about it and you will be expected to swallow it down silently. Then he'll do something dodgy and you will quite naturally react and be untrusting at which time he will play the martyr routine - how can he bear to be so mistrusted forever, should he be punished forever?! Etc.
Meanwhile, he will continue to fuck around when he can. Why wouldn't he? He's the same person who made that choice and got away with it. If you stay with him, he's gotten away with it, even if you do cry a bit and make him a bit uncomfortable for a while.
This will be your life, until he decides it's all a bit too much hassle and leaves for a pick me. Then he'll do the same to her.
Nobody is EVER happier after such a betrayal and it never improves the marriage or fixes anything. That's a sad lie people tell to try to make their massive sacrifice seem worth it. Every person who stayed with a cheater is in a relationship where they are less trusting, less happy, less secure, the relationship is always weaker. After all, it's been poisoned to death at the roots, and a new, stunted relationship has come from the poisoned mess.
Your marriage is over, assuming you want a monogamous marriage with a trustworthy person. It's just a question of how long it takes you to accept this now. If you're willing to tolerate him cheating and never being able to trust him again, you should stay.
Tell anyone you want to. If we want to be talked of well, we must behave well. That is up to you, and only you, to decide.
You should read through the Chump Lady dot com website she blows all the usual bullshit out of the water.