No; there is a reciprocity agreement between the two states, so you only file where you live.
You would have to file in MD if the employer withheld MD state taxes so you get your money back. Suggest getting the employer to withhold PA and not MD.
What exactly do you mean by "from Maryland"? Does he work in Maryland? Does he work remotely (telecommute) in Pennsylvania for a company that is located in Maryland? Or does he work at a Pennsylvania location of a company that has its headquarters in Maryland?
It makes no difference where the company's headquarters (or payroll office) is located. The employer's address on the W-2 doesn't matter. If your husband works at a company location in Pennsylvania, his income is from Pennsylvania.
What state is in box 15 of his W-2? If it's PA, his income is from Pennsylvania and Maryland is not involved.