Preheat the oven to 350 degrees F and coat a 9x5 pan with cooking spray; set aside. In a large bowl, combine the butter, brown sugar, sugar, eggs and vanilla. Mix well.
In a medium bowl, combine flour, baking soda, baking powder and salt and mix well. Gradually add to the wet ingredients until combined. Stir in the 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 the 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. Let cool for 10 minutes before serving.