Heat oven to 375° F. Butter a 12-cup muffin tin.
In a medium bowl, whisk together the flour, cornmeal, baking powder, salt, and baking soda.
In a large bowl, whisk together the eggs, buttermilk, honey, and melted butter. Add the flour mixture and stir to combine.
Divide the batter among muffin cups and bake until golden brown and a toothpick inserted into the center of a muffin comes out clean, 30 to 35 minutes.