To elaborate a bit on @Hal_Al 's answer:
Reciprocity means that PA residents who work in MD do not have to pay MD state income tax on their W2 income. That income is taxed only by their home state of PA. Hence PA residents cannot claim an "other state credit" for MD taxes unless they have income from MD other than W2 work income.
Your husband's employer should not be withholding MD taxes from his pay. If they are, then he should file MD Form MW507 with his employer in order to claim exemption from MD withholding. Here's a link to that form:
https://www.marylandtaxes.gov/forms/current_forms/mw507.pdf
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
