Line the bottom of a 13 x 9-in dish with 1 bag of the Chessman cookies.
In a large mixing bowl, combine the milk and pudding mix. Blend well using a handheld electric mixer.
In another smaller bowl, place the room-temperature cream cheese and sweetened condensed milk. Using the electric mixer, mix until completely smooth.
Add the cream cheese mixture to the pudding mixture and with a large wooden spoon, stir until well blended.
Using the now-empty bowl you used to mix the cream cheese and condensed milk, place the heavy whipping cream, sugar, and vanilla extract and whip with the electric mixer until it reaches medium-stiff peaks consistency.
Gently fold the whipped cream into the mixture in the large bowl.
Slice the bananas into the mixture, and stir gently to incorporate.
Pour the mixture over the cookies, and smooth it out.
Place the remaining cookies in the 2nd bag over the top.
Cover with plastic wrap and refrigerate until ready to serve or for at least two hours.