Legal Question in Immigration Law in Maryland

Before talking about your husband's citizenship, it sounds like what he's looking for is permanent resident status (aka a green card). If he overstayed a non-immigrant visa (as opposed to illegally entering the country) he should be able to get a green card by virtue of his marriage to you, a US citizen. He should not have to leave the country -- he can remain here and file for "Adjustment of Status". There are quite a few USCIS forms to fill out (I-130, I-485, I-765, G-325A, I-864) but if all goes smoothly he should have a green card in about 5 months.

Once he's been a permanent resident for 3 years he can file for citizenship. In that case, it does not matter how he got his green card, just that he got one. No one needs to leave the country to file for citizenship.