gosh, this is definitely a hard one. It's great for you to stand by him BUT I strongly agree with the others- it can be tough to understand, but he truly need to focus on himself right now, and possibly for quite awhile (by that I mean, a year or more- for some of us it takes a long time to heal and certainly seems baffling to our partners). Al Anon - and learning about Alcoholism (and it sounds like, PTSD) is a great idea.
Non alcoholics rarely understand what us alcoholics have to learn and adjust and change to stay sober and begin recovery. And very likely, our partners have to examine their role in the relationship bc when one person is an addict, the relationship has a dynamic that changes when the person gets sober.
It's difficult to do, but accepting that time takes time, and you really can't know if the relationship will in fact work - the very best thing both of you can do now is focus on yourselves.
Take care.