Cream together margarine and sugars. Beat in pudding mix. Add eggs and vanilla extract and mix until well incorporated. Add baking soda and powder, flour, cocoa powder, and water; beat until combined. Stir in chocolate chips and 1/3 cup cappuccino chips and mix well.

Spray a 9×13-inch baking pan with cooking spray. Transfer batter to pan and level with spatula. Preheat oven to 350 degrees Fahrenheit (180 degrees Celsius).

In a separate bowl, mix together all cheesecake ingredients. Spoon over brownie batter; swirl to marbleize with a spoon. The brownie batter does not marbleize easily; you can also just leave the cheese layer on top if desired. Sprinkle with remaining 1/3 cup cappuccino chips. Bake 45 minutes and allow to cool before cutting into squares.