Preheat oven to 350 degrees F. Lightly spray a 9 by 13-inch baking pan with butter-flavored cooking spray; set aside.
In a medium bowl, combine brownie mix, 2 eggs, vegetable oil, and mudslide drink. Mix well to combine. Transfer to prepared baking pan and set aside.
In a medium bowl, combine instant coffee and 1 tablespoon of hot water. Stir together until all the coffee has dissolved. Add cream cheese, sugar and remaining egg. Using an electric mixer beat on low speed until smooth. Fold in chocolate chips. Spread over brownie mixture. Use a butter knife to cut cream cheese mixture into brownie mixture for a marble effect.
Bake in preheated oven for 40 to 45 minutes. Remove from oven and cool completely.