Combine milk and pudding mix in a bowl. Whisk for 2 minutes.

Combine condensed milk and cream cheese in a separate bowl; beat with an electric mixer until smooth. Fold in whipped topping. Slowly fold in pudding mixture.

Layer 1/2 of the cookies in the bottom of a 9x13-inch pan. Top with 1/2 of the bananas, 1/2 of the pudding mixture, remaining bananas, remaining pudding mixture, and remaining cookies.

Chill for 2 hours before serving.