My husband workd in SC and I work in NC. We live in NC. Why are we having to pay NC taxes and not SC?

You should be paying SC income taxes on your husband's SC source of income. Your husband's employer should be withholding SC tax from his pay check. Your husband files SC's non-resident tax form (SC1040 and schedule NR). Then you file NC tax return as residents, and take a credit for taxes paid to SC.