Get rid of the "aisle" in both houses (with Dems on one side and Reps on the other) and make all congresmen sit in order of seniority, with the most senior person at the front left (as you face into the chamber) and least senior person at the right rear. You'd end up with members of both parties sitting side by side.
Current rules in the House have no assigned seating at all. The Senate does have assigned seating, but in both houses, the groups are divided along party lines.
Forcing them to 'mix it up' would require them to get to know each other (and, dare we hope, respect each other), and might lead to cooperation and collaboration between members of both parties.
For more info on seating rules in congress, visit http://www.thecapitol.net/FAQ/Congress_Seating.html