Empty pudding mixes into separate medium bowls. Add 1-1/2 cups milk to each; beat with whisk 2 min. Add peanut butter to vanilla pudding; beat until well blended. Stir 1/2 cup COOL WHIP into pudding in each bowl.
Spoon chocolate pudding mixture into 2-qt. serving bowl; cover with layers of half each of the remaining COOL WHIP and chopped cookies. Repeat layers, using vanilla pudding mixture.