How does dual-military work whenever the spouses are in different military branches?

USAF and USMC are not colocated anywhere below COCOM level, where you would not work until at least CPT or MAJ, and both of you getting the same at the same time would be unlikely.
The closest the USAF and USMC get are Guam, Okinawa and Hawaii, then:
Joint Base Andrews and Quantico at 42 miles.
The odds of getting any of those combinations at the same time are very slim.

You two should seriously consider joining the same branch, so that you have a formal program for getting stationed together.

Throughout my entire career, I only had two assignments where I was stationed with Marines (USCENTCOM/HQ and Misawa AB Japan). Assignments together could be possible but it will severely limit your options. My suggestion is to pick a branch you can both be happy in and commission there. The odds of you being stationed together would be much higher.

I’m just wondering you are in the army NG already why switch branches and hit stay army? Why you two won’t commission in the Same branch? It will be hard due especially if you can’t find a base near each other cause how can you live together in you not even stationed together?