Pour 3/4 c of milk in a medium mixing bowl. Add chocolate pudding mix and beat with a wire whisk for 1 minute. Gently stir in half of the whipped topping. Spoon mixture into crust.
Mix remaining milk in another medium bowl. Add white chocolate pudding mix and beat with wire whisk for 1 minute. Gently stir in remaining whipped topping mix. Spoon on top of other pudding mixture in crust.
Refrigerate for at least 4 hours. Store in refrigerator.