It depends. Likely you will file part-year returns in the state you are residents of while military and then the state you actually move to with the intention of staying there.
For example you and spouse from 1 Jan to 1 Dec are active military with spouse, you would use your home of record state as your resident state for that period and file a joint return using the military rules as in the past. If you then go to another state for training it is likely not going to be your resident state however each state has it own laws for filing status based on time/reason you are in the state. If the state has an income tax you would likely file as married separately and nonresident in that state.
Assuming your wife stays and after training you plan to go back to your current state, that becomes your resident state as of 1 Dec. You would file a joint part-year resident return for that state. You would also typically claim a credit for taxes paid to another state on that resident return to mitigate any taxes paid to the state you file as nonresident in for the training period.
The easiest way to file both joint and separate returns is to use a TurboTax desktop product which allows up to 5 different returns to be completed. You would create/file your joint federal and state returns and then create a "Mock" federal separate return with only your income to allow you to complete a separate state return. You will need to print/mail that separate state return.
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