Preheat oven to 350 degrees F. Grease a 9-inch loaf pan.
In a medium bowl, sift together flour, baking powder, baking soda and salt. Whisk in chocolate and peanut butter chips until combined.
In a large mixing bowl, using a mixer on medium speed, beat together banana and peanut butter until creamy, about 1 minute.
Beat in granulated sugar and brown sugar until creamy, about 1 minute.
Beat in eggs and vanilla until combined.
Reduce mixer speed to low and gradually beat in flour mixture, alternating with milk, until well combined (about 2 minutes).
Divide half of the batter into medium bowl; sift in cocoa powder, and beat until combined.
Alternate spoonfuls of banana batter and chocolate batter into the pan. When all the batter is in the pan, swirl a knife sparingly through the batters to marble them. Sprinkle with additional chocolate and peanut butter chips, if desired.
Bake for 60-65 minutes or until bread pulls away from pan, is well risen, deep golden brown, and a toothpick inserted comes out with moist crumbs attached. Cool on a wire rack for 1 hour; run a knife around outer edges and invert onto wire rack to cool completely before slicing.