Preheat the oven to 350 degrees F (175 degrees C). Grease a loaf pan.
Mash banana in a large bowl. Whisk in eggs, sugar, honey, oil, and vanilla extract.
Combine whole wheat flour, all-purpose flour, cinnamon, baking soda, baking powder, and salt in a separate bowl. Stir into the banana mixture until batter is moistened.
Stir zucchini, carrot, and chocolate chips into the batter until evenly distributed. Pour batter into the prepared pan.
Bake in the preheated oven until a knife inserted into the center comes out clean, 50 to 60 minutes.