Set 13 x 9 pan in a 15 x 10 pan and carefully pour in enough water to reach halfway up the sides of the 13 x 9 pan. Remove 13 x 9 pan and carefully place 15 x 10 pan in oven. Preheat oven to 325 degrees.
In a small mixing bowl, melt 1/2 cup semisweet chocolate and 1/2 cup milk chocolate chips with 4 tablespoons butter in microwave. Set aside to cool to room temperature.
Measure and set aside 1 cup of the dry cake mix to use in the cheesecake filling.
Coat 13x9 pan with cooking spray. Line with parchment paper and coat again with cooking spray. In a large mixing bowl, melt 3 tablespoons butter in microwave. Mix in remaining cake mix and 1 egg with a fork. Press the crumbly mixture into the bottom of the 13 x 9 baking pan.
In the same large mixing bowl, blend cream cheese, sugar, vanilla, and salt thoroughly. Beat in sour cream and melted chocolate until smooth. Beat in reserved cake mix until well blended. Scrape down sides and add eggs 1 at a time, beating on low after each addition just until incorporated.
Spread filling evenly over crust. Use oven mitts to carefully place 13 x 9 pan in 15 x 10 pan already in oven. Bake for 55 minutes, or until center still jiggles slightly. The cheesecake firms up as it cools.
Remove from oven and immediately run a sharp paring knife around the edges of the pan to separate the cheesecake from the sides of the pan. Let cheesecake cool in water bath on a wire rack for 15 minutes. Then remove 13 x 9 pan to wire rack to cool completely. Loosely cover cheesecake and refrigerate overnight.
To serve, let cheesecake stand at room temperature for 20 minutes for the best flavor.