Preheat the oven to 325 degrees F (165 degrees C). Coat a 9x4-inch loaf pan with cooking spray.
Whisk together flour, baking powder, baking soda, and salt in a medium bowl; set aside.
Beat together sugar and butter with an electric mixer in a large bowl until smooth. Add mashed bananas and mix until combined. Add eggs, one at a time, beating well after each addition. Stir in milk and vanilla.
Stir in flour mixture, walnuts, and chocolate chips until just incorporated. Pour batter into the prepared loaf pan. Tap pan on the counter to release any air pockets.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 1 hour and 10 minutes. Let rest in the pan for 15 to 20 minutes. Remove bread from the pan, then slice and serve.