Welcome. And you have a tough choice ahead of you.
The 100's of years of collective wisdom on this forum suggests your BF will most likely not recover. He certainly won't do it on his own. And you won't be able to make him do anything.
I am very familiar with the military and their programs. As long he seeks help BEFORE there is a problem, like a DUI or work related issues, then he will face no consequences with the military. If he has a DUI or other alcohol related event, they will send him to rehab, and then discharge him most likely. There are some exceptions for very young soldiers. After a second or 3rd tour, he will be discharged.
If you read through the posts, you will see a re-occurring message from me.
Leave him now. Move on and find a man with no alcohol issues. If you choose to stay, he most likely will not stop drinking. Will definitely spend a lot of your combined income on alcohol. And if he stays in the military, it will eventually catch up. Even without an official "incident" in his record, his poor performance after drinking will eventually catch up to him and others will advance over him. I see it every day.
You were not put on this earth to "fix" alcoholics. They can't be fixed. They are broken. They prey on nice, kind, loving people like you. And in the end, they make both your lives miserable. Just read about them here. Find me one post where any of us left an alcoholic and wished they did not.