My spouse lives in DC but works in Virginia. Do we need any additional state filings because of this? Also, can we still file jointly on our federal and state returns?

DC and Virginia have tax reciprocity. This means that if you live in DC and work in Virginia, you will only have to pay tax to DC. 

Generally, no Virginia return is required. However, if your spouse paid any taxes to Virginia, you would need to file a Virginia return to get back the tax that was paid. 

If you both live in DC, you would just need to file your federal and DC returns and use the same filing status for both returns.