Preheat the oven to 350ºF. Spray a loaf pan with cooking spray.
In a medium bowl, whisk together the all-purpose flour, whole wheat flour, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat sugar and butter on medium speed until creamy.
Beat in eggs and banana.
Add the flour mixture in about three parts, scraping down the bowl and beating until smooth after each addition.
Using a rubber scraper, fold in the walnuts and chocolate chips.
Pour the batter into the prepared pan and bake 55 minutes or until a toothpick inserted in the center of the loaf comes out clean. Allow the bread to cool ten minutes in the pan, then turn it out onto a wire rack to cool completely.
The bread will keep, wrapped tightly in plastic wrap, at room temperature for three days.