Not sure about baseball, but the DC Parks and Rec league runs softball season in spring (already underway) and summer. Usually though you need to find a team already in existence, which means word of mouth.
There are also church leagues and the leagues that play on the Mall near Capitol Hill (if that still happens), but again, you need an "in" there. A lot of trade associations have them.
Your best bet might be to investigate one of the leagues and form your own team through an office.
Most co-ed leagues are either 5 men and 5 women (you'll want 6 and 6 for reserves) and play 1-and-1 count at bat, and if you walk a man in front of a woman he gets second base. Some leagues (the Metropolitan Media Softball League in Montgomery County) play 7 men and 3 women.