Preheat oven to 350 degrees F (175 degrees C). Grease and flour two 9x5 inch loaf pans. Whisk together the all-purpose flour, whole wheat flour, flax seed, cinnamon, salt, baking powder, and baking soda in a bowl until evenly combined; set aside.
Beat the eggs, vanilla, white sugar, brown sugar, applesauce, and vegetable oil in a mixing bowl until smooth. Fold in the flour mixture, carrots, zucchini, cranberries, and walnuts until no dry spots remain. Divide the batter between the two prepared loaf pans.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 60 minutes. Cool in the pans for 10 minutes before removing to cool completely on a wire rack.