Preheat the oven to 350°F (175°C) and line a 12-cup muffin tin with paper liners.
In a large bowl, whisk together the whole wheat flour, all-purpose flour, baking soda, baking powder, salt, cinnamon, and pumpkin pie spice.
In a separate medium bowl, combine the mashed bananas, pumpkin purée, maple syrup, egg, melted coconut oil, and vanilla extract until smooth.
Incorporate the wet ingredients into the dry ingredients using a spatula, stirring until just combined to avoid gluten development.
Distribute the batter evenly among the 12 muffin cups.
Bake for 18 to 22 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Let the muffins cool in the tin for 5 minutes before transferring them to a wire rack to finish cooling.