Preheat oven to 350 degrees F.
Grease two 8-inch loaf pans.
In a medium bowl, sift together the flour, baking soda, baking powder, salt, and cocoa powder. Set aside.
In a large bowl, whisk together eggs, sugar, applesauce, vanilla, and bananas.
Add the dry ingredients to the wet and mix until just combined. Stir in the chocolate chips. You may reserve some to sprinkle on top of the batter.
Bake loaves for 45 - 60 minutes, until a toothpick comes out with only a few crumbs attached.