Several months before we separated and ultimately divorced, I calmly announced one night that until we got things figured out (ie, he succeeded in getting sober and we fixed our marriage) there would henceforth be a moratorium on sex. ie: I wasn't interested, so don't bother asking.
While pulling a page from the UN playbook might seem odd, I figured I'd just deal with him like North Korea and declare sanctions. It worked for me, but he was never violent and was mostly a passive object that didn't really do anything. At all. Well, drink and vomit, but not much else. I also had a great deal of power in the relationship, unlike most, and he never pulled the affair card. (I didn't, and neither did he.) I figure his "other woman" was the booze.
Good luck.