Preheat oven to 400*. Lightly coat a 12-cup muffin pan with nonstick spray or line with paper liners.
In a large bowl, stir together the bran, orange juice, honey, and molasses. Set aside for about 5 minutes.
In a medium bowl, stir together the unbleached or all-purpose flour, whole wheat flour, baking powder, baking soda, and salt.
Stir the applesauce, egg whites, and orange peel into the bran mixture. Add the flour mixture and stir just until combined. Fold in the dates.
Divide the batter evenly among the prepared muffin cups. Bake for 18-20 minutes, or until a toothpick inserted in the center of a muffin comes out clean. Cool in the pan on a rack for 5 minutes. Invert onto the rack and serve warm or at room temperature.