Mix cookie crumbs and butter; press onto bottom of 9x13-inch dish. Refrigerate 10 minutes. Meanwhile, beat cream cheese, sugar and 2 Tbsp. milk with mixer until well blended. Add 1-1/4 cups Cool Whip; mix well. Spread over crust.
Beat pudding mixes and remaining milk in large bowl with whisk 2 minutes. Add peanut butter; mix well. Spread over cream cheese layer. Let stand 5 minutes or until thickened. Cover with remaining Cool Whip. Refrigerate 4 hours or until firm.