He's not going to get custody unless he can prove you are unfit.

His career is going to prevent joint physical custody. It's too unstable. And he can be deployed to a war zone.

What he will end up with is joint LEGAL custody. Which is not the same thing as joint physical custody.

His argument that you can't provide for them because you are a stay at home mom (which is going to change when you find a job) isn't going to hold water. I was a sahm when I kicked my ex out. I have custody of my kids. I'm also no longer a sahm. But I am the primary caregiver, just like when my ex and I were married.

He will probably be able to keep you from moving until he gets stationed somewhere else. Then you will be able to relocate to where you want (and don't let him tell you that you have to move to where he is, you don't and he can't force you). It would be ideal if you and he were in the same town, but his career may prevent that. Neither of you have any control over where he gets stationed.

If he has moved out, you need to get temporary custody, child support and temporary spousal support set up.