My spouse and I are both married and active duty military. We both receive military pay. I am a resident and Maryland and he is a resident in Arizona. How should we file?

[TomD8]

Presumably you and your husband will file your federal return as Married Filing Jointly.

Assuming MD is still your State of Legal Residence (SLR), you must also file an MD return.  MD gives you the option of filing a joint return or filing as married filing separately.  But MD does tax its residents' active duty military pay.

AZ does not tax active duty military pay.  If your husband's ONLY income was his military pay, and his SLR is AZ, it is not necessary for him to file an AZ return unless 1) he had additional income other than military pay; or 2) the military withheld AZ state tax from his pay.  In the latter case, he'd have to file an AZ return in order to have those withholdings refunded.

In the event he does have to file an AZ return, AZ's filing rules for an AZ resident married to an AZ non-resident are detailed on page 4 of this reference:  https://www.azdor.gov/Portals/0/Rulings/ITR14-1.pdf