Line bottom and side of 2-qt. serving bowl with ladyfingers.
Beat pudding mixes and milk in large bowl with whisk 2 min. (Pudding will be thick.) Stir in 1-1/2 cups COOL WHIP; spoon into prepared bowl. Use back of spoon to make depression in center of pudding mixture.
Combine berries and remaining COOL WHIP; spoon into center of pudding mixture.