Preheat oven to 350 degrees F (175 degrees C). Grease 2 9x5-inch loaf pans.
Mix all-purpose flour, whole wheat flour, cocoa powder, cinnamon, baking soda, baking powder, and salt in a bowl until thoroughly combined. Whisk brown sugar, eggs, applesauce, and vanilla extract in a second large mixing bowl. Stir zucchini into the liquid ingredients and beat in flour mixture until batter is just combined; do not overbeat. Gently mix in cinnamon baking chips. Divide batter evenly between prepared loaf pans.
Bake in preheated oven until lightly golden brown and a toothpick inserted into the center of a loaf comes out clean, 55 minutes to 1 hour. Cool in pans for 10 minutes before removing loaves to finish cooling on wire racks.
