Preheat oven to 180° C | 350° F. Grease a 9x5 loaf pan and set aside. Squeeze out the excess water from zucchini after grating.
In a bowl, whisk all-purpose flour, wheat flour, baking powder, baking soda, cinnamon and nutmeg.
In a large mixing bowl, beat the eggs. Add oil, applesauce, vanilla and whisk until well blended. Add sugar and whisk until combined.
Stir the carrot and zucchini into the mixture. Then add the flour mixture and gently fold until just combined.
Pour into the prepared loaf pan and bake for about 50-60 minutes or until a toothpick inserted in the center comes out clean.
Let the bread cool in pan for 10 to 15 minutes. Then move to wire rack to cool completely before slicing.