if you are travelling through DC or MD you are covered by federal interstate firearms transportation laws (see U S code 18, 926a) but that's it. Read 926a and adhere strictly to it because DC and MD don't mess around. As long as you meet the requirements of 926a you should be fine.
I live about 5 miles outside of MD and I travel through MD pretty often with a firearm, I just make sure I'm compliant with 926a, same goes for DC. If I'm stopping in either DC or MD I don't go armed, PERIOD.