There will not be "any" late filing penalty from the IRS, becuase you did not owe the IRS any money - they owed you a refund.
For the state, you will owe at least interest on your late payment of state taxes. Remember, when you file an extention that only extends your time to file the return. It does not extend your time to pay taxes, if taxes are in fact, due. Now having paid the state taxes stopped the accumulation of interest on the amount you owed and paid. You can expect the state to bill you separately for any accumulated interest if owed. If your state also assessed a late filing penalty, then I would not know how that would be handled. I don't know what state the AD/MIL person is stationed in or what their "tax home" state is, and I also don't know the SLR of the non-military spouse.
