How do I file federal joint but separate state taxes?

Generally, "yes;" however there are other factors that must be considered. If you repost here with more clarifying details on your situation with regards to the factors below, someone will be able to answer with specifics to your situation.  

Having said that, the easiest solution is for you and your spouse to both claim your home of record state as residence.  Your spouse does not need to do anything but live with you and be with you in the state on military orders.  Generally, you will file a joint federal return and a joint resident state return for your (home of record) state.  Your military pay and your spouse's income, even though earned in the state you are residing in, generally will not be considered sourced to that state. Therefore you would only need to file in one state (your home of record).    

Factor 1:  The laws of the state you are residing in.  If your spouse does not claim the same resident state as you, she does not fall under the Military Spouse Relief Act.  If that is the case she would need to file in the state you are residing in, in accordance with that state's laws and not her prior home state.   

Factor 2:  What status are you filing on your federal return?  Each state has it own rules regarding how you need to file as related to your federal filing.  Some states allow separate returns after a joint federal; others do not. Further, if you are allowed to file separately how is the other spouse's income treated in accordance with that state's laws.   

Factor 3: Your military status.  Each state has it own rules regarding how military pay is handled.  The state you are residing in and your home of record state will determine the taxability and need to file according to your situation.  Here is a link with more information on filing as active duty military and as a spouse to active duty military.