Sober Boyfriend Relapsed and Cheated

Me (38) and my sober bf (35) have been together for 6 months and are exclusive. My bf has been to alcohol addiction rehab several times. He's gotten very close to rock bottom (almost homeless and penniless). I've never dated someone with an alcohol abuse issue but was ok with it because he was back on track & doing great when we met. Early in our relationship he shared that when he drank, he turns into a monster who lies. That he hates and regrets that version of himself, which is why he's sober.

During Christmas together (we visited his family) he relapsed. It wasn't pretty. He was, in fact, a monster - angry, unhelpful, distracted, closed off. I was direct with him about implementing strategies to get better (e.g. therapy, AA, more structured daily routines etc.), some of which he is now doing. We had a good conversation and he apologized.

The following weekend, he relapsed again (I wasn't with him that weekend). He went out with friends and hooked up with someone. I know he went out because I asked him about his weekend and he admitted to drinking. I know he hooked up because a few days later he had his laptop open and I saw an iMessage with one of his friends asking about the drunk hookup. I also saw messages that he regretted drinking, that he's working on getting better, that he doesn't want to be a monster, and that making change is more challenging for an addict.

I don't know where to place the blame - him or the disease. He loves me in other ways - calls and texts, asks me about my day, remembers small details, buys me gifts, visits me etc. He does everything else a bf is supposed to do. I'm struggling with how much to blame him vs. the addiction.