1Heat coals or gas grill for direct heat. Mix beef, sausage and bread crumbs in large bowl. Shape mixture into 6 patties, about 1/2 inch thick and 3 1/2 inches in diameter.
2Cover and grill patties 4 to 6 inches from medium heat 12 to 15 minutes, turning once, until meat thermometer inserted in center reads 160º. Top patties with cheese. Cover and grill about 1 minute longer or until cheese is melted. Add bread slices to side of grill for last 2 to 3 minutes of grilling, turning once, until lightly toasted.
3Spread toasted bread with mayonnaise; top 6 bread slices with lettuce, tomato and patties. Top with remaining bread slices.