Preheat oven to 350 degrees F and coat a 9×5 pan with cooking spray; set aside. Combine the butter, brown sugar, sugar, eggs and vanilla in a large bowl. Mix well.
In a medium bowl, combine flour, baking soda, baking powder and salt and mix well. Gradually add to the butter-sugar bowl until combined. Add mashed bananas and chocolate chips. Pour half of the batter into the prepared pan. Spread softened cream cheese evenly over bottom half of the batter and top with remaining batter.
Sprinkle additional chocolate chips over the top, if desired. Bake in the preheated oven for approximately 1 hour. Start checking for doneness at the 50-minute mark. When a toothpick inserted into the center comes out clean, the bread is done.