You've received good feedback above. It kind of sounds to me as if he sort of doesn't want a serious commitment at this point. I say that because, in addition to admitting his problem, he (a) used it to explain why he didn't want things to "move forward" and (b) expressed no interest in recovery. So it kind of sounds to me as if he's telling you, straight up, "what you see is what you get." Not gonna change, and, BTW, for your own good I'm not comfortable with making a commitment.
I think he's perfectly happy to have things remain as they are, but as pointed out above, this is not a good situation for you OR your kids. And it's likely to get a whole lot worse, regardless of whether you stay or go.
Doesn't sound like a promising future if you stay with him. I'd be thinking about moving on.