If my husband and I are residents in montana but didn't work in there this year why are we paying taxes?

If Montana is his Home of Record state when he joined the military, that is his state of residence for tax purposes. For yourself, if the Montana was your state when you got married, then your State of Legal Residence is Montana also. If you wish to change this, you must take action within the military personnel office. 

Now for the non-military spouse, if you have income earned in another state outside of your State of Legal Residence (SLR), then depending on the SLR and the state that income was earned it, you may not have to pay that state any taxes on it. This is covered in the MSRRA (Military Spouse Residency Relief Act) of whatever state you earned the income in, if that state has such an act. (almost all do.) If this is the case, you must take action within the military personnel office.

As i mentioned, you might wish to change your Home of Record state or State of legal Residence but if you move around a lot, this may not be the best choice to make because you would need to keep changing.  Also the tax codes and rates vary from state to state and many states may not be as favorable as Montana tax wise.  However if you live in a state that doesn't have a state income tax, then the change of state is an advantage for both of you.

As Montana residents, your husband's active duty military pay is exempt from Montana income tax, but your income is not exempt - regardless of where you earn it.