BEAT cream cheese in large bowl with mixer until creamy. Gradually beat in milk. Add dry pudding mixes. Beat 2 min. Gently stir in 1 cup COOL WHIP. Remove 1-1/2 cups pudding mixture; cover. Refrigerate along with remaining COOL WHIP later use.
LINE 8-inch round pan with plastic wrap. Cut ladyfingers crosswise in half. Stand about 1/2 of the ladyfingers around edge of pan, with rounded ends down and flat sides facing center. Spread remaining pudding mixture onto bottom of pan; cover with remaining ladyfingers, rounded-sides down. Cover. Refrigerate 3 hours.
INVERT dessert onto serving plate. Remove pan and plastic wrap. Spread side of dessert with 1/2 the remaining whipped topping, leaving rounded tops of ladyfingers unfrosted. Spread top of dessert with reserved pudding mixture and remaining COOL WHIP. Top with chocolate curls and raspberries. Keep refrigerated.