Could it be that your SS doesn't avoid discipline becuase it's one way to get attention? I've found all of us, kids & teens especially, like to be noticed, talked to, spent time with. If that's not happening in a positive way, it's taken any way they can get it.
Is your husband going out of his way to spend time with his son? It's not easy, we are busy, teens are beligerant and say they don't want to spend time with us, etc. But they do. They want to be encouraged when they do a good thing. They want their family to be proud of them. They want to feel a sense of accomplishment. They will respond to positive expectations.
It's very hard for me to get my husbnad to understand this with our teens, particularly our son. It's easy for me to spend time with my daughter and get to talk and share our values in terms of morals, dreams for her future, expectations with boys, school, home - becuase she & I like to do the same things. Its much different with my son. He & I only get to talk when we're in the car going somewhere. So I make a point have him with me on a long drive every so often. And I make sure he knows I am proud of him for certain things (he's taken on chores around the hosue and no longer needs our insruction, he helps with a children's program at church, etc.) I tell him what we expect of him, I tell him I know he can and will fill those expectations and that no matter what I'll always love him. I ask lots of questions about what he hopes for in the future, I ask him about the things he likes to do (video games, playing basketball & baseball), etc.
Sounds like your SS may need some of that. It's said that women want to be loved, men want to be respected. So if he needs money assign him some chores around the house that are at a higher level - and offer to pay him. That will help him gain self-respect. If he doesn't have a job encourage him to get one.
Finally, don't leave your handbag in a place that's so tempting. If you know he's taking money and you keep leaving it there for him it seems that you're trying to catch him instead of trying to help him. The tough thing about step-kids is that you often have no rights in terms of discipline, but you still ahve all the responsibilities. I would have a talk with him though - without outright accusation. I would tell him that money has been missing out of your bag and you're certain it occurs when you go to bed. Tell him that you can't imagine it would be his action, and ask if he had a friend over that might have done it. He probably won't admit it - don't expect that he will. But tell him that you expect he'll make sure that none of his friends go in your bag, tat you're glad you can count on him to do the right thing. If nothing else it will make him feel remorse.
The keep telling yourself it's only 6 more months. I expect you'll see a change in his character once he's in the reserves. And BTW - you never know about college. I was a C- D student in high school (due to a number of different things) and I excelled in college came out with a BS in Economics and Business. I got out of the town I grew up in, I got out from under the shadow of my golden boy brother (one year older than me) and I matured. You never know!