Preheat the oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners or grease the cups lightly.
In a medium bowl, whisk together the all-purpose flour, baking soda, baking powder, salt, and ground cinnamon until well combined.
In a large bowl, whisk the granulated sugar, brown sugar, and vegetable oil until combined.
Add the eggs one at a time to the sugar and oil mixture, whisking well after each addition.
Stir in the vanilla extract and mashed bananas until fully incorporated.
Add the grated zucchini and milk to the wet ingredients and mix until evenly combined.
Gradually add the dry ingredients to the wet ingredients, folding gently with a spatula until just combined. Do not overmix.
Divide the batter evenly among the 12 muffin cups, filling each about 3/4 full.
Bake in the preheated oven for 22 to 25 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Remove the muffins from the oven and let them cool in the pan for 5 minutes.
Transfer the muffins to a wire rack to cool completely before serving.