Welcome Heart,
You've gotten a lot of good feedback from the others. I've been out of the military for quite awhile, so things have certainly changed since "back in my day." Getting kicked out (meaning dishonorable discharge? discharge under other than honorable conditions? bad conduct?) for a single DUI seems extreme to me given what I've seen of military discipline, especially for alcohol-related offenses. Showing up drunk for PT was commonly blamed on "strong aftershave" and the soldier would, after sweating it out, be instructed to drive home, shower and drink water (the cure for everything!).
The only soldiers I knew of who were summarily discharged had failed drug tests. For NCOs it was an automatic DD, for junior enlisted it was at the command's discretion.
You now know that there are a lot of things he's kept from you, not saying he's doing drugs, but I suspect there's more to his issues than meets the eye. My ex seemed absolutely golden when we met and deployed together, and I felt I owed it to him to stay and support him no matter what because of all he'd been through. The only thing my "support" did was help him spiral down without consequences. He's right that he's not ready to get married. He's got a lot of sorting out to do in his own life first.