I'm ex military and I've attempted suicide since and at times still am. I became dependent on alcohol too as a retreat from reality / crutch. It didn't help and it made things worse.
Does he realise that alcohol is a long term depressant (I didn't) and that far from helping, alcohol is just masking the issues and giving him new ones. The terrible with the military is that the culture is very alcohol orientated to a degree that heavy drinking seems normal and it took me a long time to realise I had a problem and it wasn't normal.
I decided to quit when I realised I had an issue. It was not easy and I did so after a few attempts. I've now been sober for about 8 years and it's been one of the best things I've done. At first it makes emotions raw and you feel a bit naked, but you (your brain) get used to it over time and you learn to cope without the support and life is -eventually- better. You also better, you're less depressed, you've more money, less moody, healthier and many other benefits from no longer drinking what is basically a poison.
He's done well realising he's got a problem. He now needs to get help for that addiction as it's a very hard one to break (believe it or not harder than heroin) and it can be dangerous if you're physically dependant (again more so than heroin). I got help from an alcohol forum for people who are quitting, but in his case he might need medical help due to the PTSD and suicide risk. He probably needs proper counseling for the PTSD as that provided by the military used to be lousy (it might have improved since I left).
It took me a few attempts to quit and it was hard and it felt raw and exposed and I lost a social outlet (and friends or drinking buddies rather than friends), but in the end it was a lot better. I had to learn grow up and stop hiding behind alcohol and face the world and my inner problems.
So, he's done well realising he's got a problem and now he needs to get help and do something about it. Alcohol dependence is not an easy thing to kick and asking for help to kick it is not a sign of weakness, it's a sign that you're starting to take control of your life.
As for the suicidal thoughts, he needs help for that. In the short term, make sure there's not anything around that would enable him to hang himself (like rope) and make sure he realises that it would devastate you (some people think it would be the best for everyone). Suicidal attempts tend to be spur of the moment when they actually happen, so ensuring there's not the stuff to do it in the house is important. If there are signs he's planning it, like buying the stuff, then call someone as that's when it's turned from a thought into a decision. You could even get a lock for the shed and keep the key hidden. It might sound dumb, but if it helps him pause and consider and makes things harder, then it's worth it. My attempts were generally with stuff that was at hand. The times I planned were generally easier to get help for. If he does consider it, then I found the Samaritans to be fantastic and I owe them my life.
I hope that helps. He's not me at all, but we ex squaddies have to look after each other, as imo the military didn't.