If your husband really wants to experience some military culture, you should try to have a meal at the Army/Navy Club. I say "try" because it is a members-only club, but if you belong to one of the reciprocal clubs or know a member, you can get in. There's a tremendous amount of history there.
You can also check out the Old Guard Museum. The 3rd Infantry Regiment, or Old Guard, is the oldest continuously serving infantry regiment in the Army. They do the ceremonial details for the Military District of Washington, including Arlington.