Ok, so you're in my exact situation this time last year. I have been dealing with the JAGs on and off for several months trying to get this scenario resolved. Let me give you advice from my experience so you don't have to make the same mistakes.
A few general pointers:
It is illegal for them to not allow you to resign your lease. This is discriminatory, and you should inform your landlord of this. If needed have him get the JAGs involved.
Make sure you keep a record of all communication going forward. Just incase something goes wrong.
Both of you go look up the Servicemember's Civil Relief Act. This is the federal law that details many benefits for military members and their family particularly regarding leases (both real estate and vehicular).
Again, your scenario is pretty damn close to what I went through. So I'd recommend you know and do the following:
First, under the SCRA, it does not matter if you signed the lease unmarried, as long as you are married and on his orders when you go to break it, it applies to both of you. My fiancee at the time signed a lease with me last spring. I commissioned and got married in June. Got her placed on my orders for Pensacola, terminated six months later and didn't have a problem with that part.
Second, make sure your landlord knows he's in the Navy. My landlord tried to fight me one this since I put an internship on my initial application, and that employer was no longer my current one.
Third, if you don't know how many months you'll be there, or you can't get a short term lease, just sign for an additional year. I know it seems like a bit of a shitty thing to do, but sometimes it is what has to be done to give military members the flexibility they need when transferring to different schools. Particularly with flight students as he will be in Pensacola for 3-6 months, transfer to primary, transfer to intermediate 6 months later, then transfer to advanced 6 months after that. It allows for some peace of mind knowing that even though you'll be in one place for an indeterminate short amount time, you'll have a place to live should plans get altered or delayed.
Fourth, what terminating your lease under the SCRA does is essentially bring you to the point where you'd normally be moving out. What that means is anything you'd normally do moving out of an apartment you still have to do, including having your security deposit returned. You are not required to find new tenants, pay realtor fees, or be fined. It might seem a little rude, but when you give your previous landlord your forwarding information, make it clear that your expecting to get your security deposit back.
Please feel free to ask me any questions. I'm not a lawyer, but I have become decently familiar with this.