Prepare and bake the red velvet cake according to the package directions in a 9x13-inch pan.
Allow the cake to cool slightly, then use the handle of a wooden spoon to poke holes all over the cake.
In a mixing bowl, whisk together the cheesecake pudding mix and cold milk until smooth.
Pour the pudding over the cake, spreading it evenly to fill the holes.
Refrigerate the cake for at least 1 hour to set.
Spread the thawed whipped topping over the chilled cake.
Sprinkle the crushed chocolate sandwich cookies on top.
Slice and serve chilled.