op I’m sorry you are in this situation.
Some mentioned it may have been a one night stand suggesting that isn’t a series of decisions but every act of cheating features hundreds of tiny decisions.
You start by chatting to someone, then push that to flirting at that point you KNOW you are overstepping. Then each subsequent choice is a choice to be unfaithful. No one goes from sitting at a bar chatting to having sex (presumably in another place) without many, many small steps in between.
A one night stand is easy to avoid if you stop the minute you start flirting. Any affair isn’t a mistake, it’s a choice.
I see your husband was longer term. It’s still a series of choices.
I say this regularly on here but I am faithful for me. I chose to say my vows in front of my family and friends and my words mean everything to me. If my word is meaningless then who am I. My husband (annoying at times) is not powerful enough to make me cheat or remain faithful. He is the collateral damage to my choices. But I choose to be faithful for ME not him. I have to look at myself in the mirror every day and I want to like who I see. My values matter to me.
Op if your partner has cheated it’s never due to you. Nothing you do (or don’t do) can make someone cheat or stay faithful.
How are you feeling op? Do you have real life support?
But I would tell her husband. Many on here disagree. But two parties fighting for their marriage and two betrayed spouses on the look out makes it harder for them to remain in contact. I would not tell my husband I was telling him, I’d contact him and meet him and show evidence. If you husband moans about feeling unsafe afterwards, more fool him for putting himself in a position where that is a possibility.
Look at the surviving infidelity website.
How can he assure you it will never happen again? What does that mean? What has changed? Why is he now capable of keeping his word but last month he was incapable?