Lightly spray a 9x9" pan with non-stick baking spray. Set aside.
In a food processor, crush the chocolate cookies. Add the melted butter, and pulse a few more times in the processor to combine. Pour the crumb mixture into the 9x9 pan, and press firmly and evenly into the bottom of the pan. Refrigerate or freeze the crumbs, just to get the crust to set.
To the cool crust, pour the hot fudge sauce and spread evenly. Refrigerate while you mix the filling.
Using a hand or stand mixer, begin mixing the peanut butter filling. To a mixing bowl, add the room temperature cream cheese and powdered sugar. Beat until creamy. Add the peanut butter and mix until completely combined. Mixture will be thick.
Slowly add in the milk, and mix until smooth, making sure to scrape down the sides of the bowl.
Lastly, add in the thawed whipped topping, a few scoops at a time until combined. Mixture will be light and creamy. Spread onto the top of the hot fudge covered crust. Top with the chocolate and peanut butter chips.
Cover with plastic wrap and refrigerate for at least two hours for the filling to set. Slice into 16 square bars.
Keep any leftovers refrigerated for up to one week.