Mix cookie crumbs and melted butter in a bowl with a fork. Press into the bottom of a 9x13-inch baking pan to make the crust. Place in the refrigerator.
Combine cream cheese, sugar, and vanilla extract in a bowl; beat with an electric mixer until creamy. Fold in 1 1/2 cup whipped topping; spread over crust. Place in the refrigerator.
Whisk milk and chocolate pudding mixes in a bowl until thickened. Let sit for 5 minutes. Spread over cream cheese layer. Spread remaining whipped topping over chocolate pudding layer. Sprinkle chocolate chips evenly on top.
Freeze until set, about 1 hour, or refrigerate for 4 hours.