Preheat the oven to 400 degrees F (200 degrees C). Grease 12 muffin cups or line with paper liners.
Stir whole wheat flour, rolled oats, sugar, baking powder, baking soda, and chocolate chips together in a bowl. Make a well in the center.
Whisk eggs in a separate bowl until frothy; mix applesauce, skim milk, and banana into eggs. Pour wet ingredients into well made in flour mixture; stir just to moisten. Batter will be lumpy. Fill the prepared muffin cups about 3/4 full.
Bake in the preheated oven until a toothpick inserted into the center of several muffins comes out clean, 16 to 18 minutes. Cool in pan for 5 minutes before removing to finish cooling on wire racks.