Preheat oven to 350 degrees 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.
Substitute JELL-O Vanilla Flavor Instant Pudding & Pie Filling for the white chocolate flavor pudding and pie filling mix.
Assemble dessert in 13x9-inch disposable foil pan. Wrap tightly in plastic wrap and refrigerate as directed. Store in an insulated cooler packed with plenty of ice or frozen gel packs to take along to your party destination. Uncover and top with the marshmallows just before serving, then broil as directed.