Heat gas or charcoal grill. Cut 8 (12x12-inch) sheets of heavy-duty foil. Spread cut sides of buns with mustard-mayonnaise spread.
On bottom halves of buns, layer cheese, salami, turkey and bell pepper. Cover with top halves of buns. Place sandwiches on foil. Wrap each packet securely using double-fold seals, allowing room for heat expansion.
Place packets on grill. Cover grill; cook over medium heat 8 to 10 minutes or until thoroughly heated. Carefully open packets to allow steam to escape.