I'll be honest, I've known a couple of couples for whom cheating is just not a deal-breaker. Both of them have been at times, indiscreet. One couple married about 40 years (man was always on the prowl, don't know about her), the other i think married about 50 years (man had numerous women on the side, woman actually had a long-term, romantic liaison with someone) . You could do some therapy around this and hopefully get some clarity about what it means to YOU.
I was married to an alcoholic for 25 years. He died. I loved him, but in retrospect, I wish I had divorced him when I realized he would never change. Starting over with a new apartment, a new set of friends, managing my limited budget on my own, career decisions would have been a heck-of-a-lot easier at 35 than 20 years later. And by my fifties, I had decided to leave him...got home *that night* and he told me he was terminally ill. We're not supposed to tell you what to do, but from where I sit, your husband's infidelity is only one problem. His addiction is another. let me tell you when AH died and I was free, there weren't a lot of available men in my age range. The ones that didn't already have relationships, well there were good reasons for that. The widowers knew it was a buyer's market for them. They could pick and choose...many wouldn't date anyone past her mid-forties, even if they were in their sixties or older.
I'll tell you about my Dad, who was a functional alcoholic until after he retired. The drinking got the better of him one night, and he drove drunk. There was an accident, and he killed someone. Dad went to prison at 76 years old. Prison. Luckily, the judge took pity on him and it was a relatively short sentence for vehicular manslaughter. Mom drove four hours every week to visit him. The victim's family filed a civil suit, and my parents lost half their life savings in it.
I'll write it again: Half their entire life savings. Gone. In their seventies when they needed it. No lawyer would take their case to defend them.
If you intend to stay married to an addict, You would be wise to make sure your auto insurance is top shelf. Just saying. And this is coming from a woman who compared her fiance's drinking to Dad's behavior and thought "Eh, he does like his beer, but so does Dad."