You can still file a joint federal income tax return. New Hampshire doesn't have state income tax (except for interest and dividends), as you know. However, Maine does. If it works out better for your tax situation, your spouse (who resides in Maine) can file as Single on the state tax return. According to the Maine Revenue Services website:
"If you filed a married joint federal income tax return, but you and your spouse have a different residency status, you may be able to use Schedule NRH. Also, if you and your spouse are both nonresidents or safe harbor residents of Maine, but only one of you has income from Maine, you may use Schedule NRH.
By filing Schedule NRH, you are choosing to be taxed as a single individual on your Maine tax return, even though you filed a joint federal return."