PREHEAT oven to 350°F. Finely crush 40 of the wafers; place in medium bowl. Add butter and sugar; mix until well blended. Press firmly onto bottom of 13x9-inch baking pan. Bake 8 min. or until lightly browned; set aside.
POUR 1-1/4 cups of the milk into medium bowl. Add dry chocolate pudding mix. Beat with wire whisk 2 min. or until well blended. Spread over crust; top with remaining 24 wafers. Pour remaining 2 cups milk into large bowl. Add dry white chocolate pudding mixes. Beat with wire whisk 2 min. or until well blended. Gently stir in whipped topping. Spread over wafer layer in pan. Refrigerate at least 3 hours or until set.
PREHEAT broiler just before serving. Top dessert evenly with marshmallows. Broil 1 min. or until marshmallows are puffed and lightly browned. Sprinkle with chocolate. Cut into 24 squares. Serve immediately. Store leftover squares in refrigerator.