This is coming from a recently dismissed mistress here, also from someone who many years ago had her husband cheat on her. He lied about it at first, I gut instinct knew it. Then I found evidence, confronted, he still lied, but then eventually I drilled it out of him. He confessed and sounds like you didn't have to drill him long before he admitted it.
This comes to mind for me... it's my personal belief a man doesn't cheat just because of opportunity. Every man has opportunity at some point, not to sound cruel but he was probably feeling something missing in his life - excitement, youth, relationally, etc... but trying to fill it. That usually isn't something that just pops up one episode of times and goes away once they "get it out of their system," it happens again if the hole he's trying to fill doesn't fill. May not mean he doesn't get the required stuff from you, he may have what I would call a hole in his tank, some guys the hole is big, others small but if they have one, eventually they will find themselves weak from the lack of fill, and fill it by looking for it, or simply opportunity combined with that empty "thing" he feels. So... does it make sense to say however you choose to do it, except it has to be done with him and with his complete willingness and eagerness to find out what that hole for him is and if you love him, as his wife see if there's enough honesty and true determination in the both of you to get him "healed" and mend that hole.
Second, I guess I'd say again 2nd time today, if you find yourself becoming a worse person for enduring and taking up the good fight of keeping your marriage, then it isn't worth it - now you are becoming a person that is usually scared all the time, paranoid, mistrusting, resentful, you hold in anger and then blow.... in other words if you become a better person for being compassionate and really feel you two can figure out how to battle any emptiness he may feel TOGETHER, then put your whole heart in it and love him through this and remind him not to define himself by this one instance as you remind yourself the same thing, however - if you start to become the worst version of yourself, your health declines, you can't take the "battle" and you are worse off as an individual for the wear then make that decision yourself. Only you know what kind of person you want to be and how you want to feel and if you want to endure or move on. I wish you only the best regardless of what you decide...