Preheat oven to 350. Coat an 11 x 13 pan with cooking spray.
Stir together flour, baking soda and salt in a large bowl. Set aside.
In a large mixing bowl, beat butter, shortening, granulated sugar, brown sugar and 1 teaspoon vanilla with an electric mixer until creamy. Add 2 eggs, one at a time, and mix to blend. Add flour mixture in three additions until well combined, but do not overbeat. Gently stir in 2 cups chocolate chips. Spread batter evenly into prepared pan. Set aside.
In another bowl, beat cream cheese with clean beaters until fluffy. Set aside 1/4 cup powdered sugar. Gradually add the remaining powdered sugar to the cream cheese, then beat in the remaining 1 teaspoon vanilla and the remaining 2 eggs. Beat until smooth. Stir in the remaining 1 cup chocolate chips. Pour filling over batter in prepared pan. Dust the top with the reserved 1/4 cup powdered sugar.
Bake for 40-50 minutes until the edges brown. The center should be slightly wiggly.
Let cook on a wire rack to room temperature, then refrigerate for at least 6 hours before cutting and serving.
Preparation and cooking time does not include cooking and refrigeration times.