Dual Military

My husband is in the Army, and I am planning on joining the Air Force. I was wondering if anyone here has been dual military but separate branches like this before? I’m not really too worried, I feel like I know what to expect. I’m not worried about whether or not we’ll be stationed together/see eachother, just because I know nothing is ever for sure until it happens, and to expect the worst but hope for the best. But as fair as on paper, what are the steps we need to take? One of his coworkers told him that there’s a bunch of paper work to fill out and to do it asap after I join - but this coworker is dual military both in the army. Are the steps different for different branches? How is that done? Is there anything you didn’t know/wish you had known prior?

Thanks!