IF both spouse's are claiming the same state of residence (AK in your case) the military family never indicates living in, or moving to another state when the military member PCS's and the civilian spouse goes along to the same base/region.  For tax purposes , you are always in AK.

When the military person goes to a Combat zone, he/she still doesn't "move" or live in another state, nor does the civilian spouse as long as the civilian spouse remains at the base that the Military person shipped out form ...to the Combat zone.

IF the military person PCS's to a state, and the civilian spouse does not accompany the Military person...then it may get more complicated, but as long as you remain together...you are both AK.

(when entering the Military person's info, there might be a second question about what state they are posted to, and that is OK to indicate another state...not sure what overseas posting selections they have)