Yes. In general, if you and your spouse file married jointly, MFJ, on your federal income tax return, then you and your spouse also should file married jointly on your state return either in NC or SC.; Married couples do not have to live together to file jointly.

Yes, you can file joint return.
For NC state tax return, your spouse is resident and will report his income. You are non-resident and does not have any NC income.
For SC state tax return, you are resident and will report your income. Your spouse is non-resident and does not have any SC income. Your U.S. Tax Return: Working or Living in Two or More states (http://taxipay.blogspot.com/2008/06/working-in-two-or-more-states.html)