What happens with my pay and duty station if I marry an individual in another branch of the military?

I realize you haven't been in the service that long, or had a reason to think about where all the major installations are for each branch, but you have to ask yourself, what is the likelihood that a Navy base would have an Army job for an Army mechanic, or that an Army base would have a Navy job for your future spouse.
The answer is none.
There is no official married couples program managed between branches, each component has their own. If your fiancee was Army, the Army would do what it could to put you at the same installations, no guarantees.

For the finances, you would both get BAH, nobody would get FSA unless you had kids, then the one away from the kids would get FSA.

I'm not saying don't get married, I'm just saying to prepare yourselves now to spend your entire enlistments 500-3000 miles apart, and plan smart with your money and leave time.

Alright so imma tell you this now PFC. There is only one program for dual military couples of different branches and it’s Joint Domicile. And even that barley works. There really isn’t a single program that talks between every branch for people married between different branches. It’s hard. And it will challenge you two in every single way. And really for finances it depends on who is the highest ranking of you two for certain things. But your both receive BAH, BAS and if separated most likely both of you will get it and all that. For duty stations it’s hard, it’s rare your be together and it has a lot of grey area to be honest. Hawaii is one of the few places all branches exist here with some sort of base on the island of Oahu. Your be reading a lot of navy and army regulations in your time in service together.

I have a soldier right now who is in the same situation. He is an E-4 in the Army and his, now wife, is an E-4 in the Navy. I will tell you this right now. You will NOT receive BAH/BAS/or any type of Separation Pay. Because you are eligible to live in the barracks, and your spouse does not live with you, the Army will place you in the Barracks. Point, blank, period. The Army has the Married Army Couple Program (MACP) however, thats specifically for two soldiers who get married. The Army can try their best to station you close to your spouse, however, it is not a guarantee due to the different branches situation.