Combine first 8 ingredients in a small bowl; toss gently. Let stand 30 minutes, tossing occasionally.
Cut a thin slice off top of each roll and set aside. Cut a 2-inch wide, V-shaped wedge down length of each roll. Reserve bread wedges for another use.
Drain vegetable mixture. Line each roll with a lettuce leaf; arrange ham and turkey evenly over lettuce. Spoon vegetable mixture evenly over meat and cover with roll tops.