Preheat oven to 400°F. Coat 12 muffin cups with cooking spray.
Combine whole-wheat flour, all-purpose flour, baking powder, baking soda, pepper and salt in a large bowl.
Whisk eggs, buttermilk, oil and butter in a medium bowl. Fold in scallions, bacon, cheese and bell pepper. Make a well in the center of the dry ingredients. Add the wet ingredients and mix with a rubber spatula until just moistened. Scoop the batter into the prepared pan (the cups will be very full).
Bake the muffins until the tops are golden brown, 20 to 22 minutes.
Let cool in the pan for 5 minutes. Loosen the edges and turn the muffins out onto a wire rack to cool slightly before serving.