BEAT first 4 ingredients with electric mixer until well blended. Add eggs and egg whites, 1 at a time, mixing well after each addition. Gradually add 2 cups milk, beating until well blended.
ARRANGE 9 bread slices in 13x9-inch baking dish sprayed with cooking spray. Sprinkle with half the raspberries; top with remaining bread slices. Pour cream cheese mixture over bread. Let stand 30 min. Preheat oven to 350°F.
BAKE 40 min. or until golden brown. Meanwhile, bring remaining milk just to boil in saucepan; gradually add dry pudding mix, whisking until well blended. Remove from heat; let stand 5 min. Microwave remaining raspberries in small microwaveable bowl on HIGH 15 to 20 sec. or until warm. Serve French toast topped with custard sauce and raspberries.