Pour milk into large bowl. Add pudding mix. Beat with wire whisk 2 minutes. Let stand 5 minutes or until thickened. Gently stir in 1 1/2 cups of the whipped topping.
Place 10 of the cookies on bottom of 2-quart serving bowl. Top with 1/3 of the bananas and 1/3 of the pudding mixture. Repeat layers ending with pudding mixture. Cover with remaining whipped topping. Refrigerate until ready to serve.