I don't think you can in most cases....you must each file a tax return for your Home-of-Record/State-of-legal-Residence (HOR/SLR) . Some states require couples in your situation to file MFS tax returns for that state, while others have a way to file State-MFJ and remove the non-resident spouse's income. (Desktop softwr is usually far better if you have to do this.
Only one way I know of to change the situation...when you are both posted to either one of your HOR states, the other spouse changes their SLR to be that state (the spouse making the change must be posted in that state). This requires changing Driver's Lisc...voting...bank accounts etc...anything that proves you intended to become a resident of that state...AND...requires the submission , and acceptance of a form DD2058 by your Military (Personnel/Finance dept....not sure which) BUT..I'd suggest you contact your local JAG about that, since I really don't know the fine details.
Normally a military person's HOR and SLR are the same state, but with an accepted DD2058, the SLR part becomes the new state for state tax purposes.
Another way to have the same SLR state, is that when you are both posted to the same state (even when not the HOR for either of you) you both DD2058 change to that state. For Career military, they commonly do this when posted to TX, or WA, or FL or another state without an income tax.....but others are faithful to their home state and don't want to change.
(And any military person who does do this, will need to file part-year tax returns for both states for the year of change...effective on the date of the D2058 acceptance, they "moved" from the former state to the new one)
Or if both spouses are not intending to remain in the military, it might be too much hassle and not worth the effort.
When you start your federal return, when entering the information under the Personal Info tab you will be asked the resident state question and the AD MIL question for each tax filer separately. Just select accordingly. It is VITALLY IMPORTANT that both of you claim your individual incomes for your specific state of residency, and that you properly indicate what income belongs to which tax filer. If you do that, then it will be easier on your state tax returns to exclude the income of the non-resident spouse.
Also, most states exempt military income from state taxes if you are stationed by PCS orders outside the state and earn that income while physically outside the state.
If tax filer A is "NOT" stationed in their home state, and tax filer B has non-military income in that state, MSRRA applies (sort of) to that non-military income under another program. I'll go into detail only if necessary. But I would need to know the HOR of each tax filer and the state where you are both currently stationed.