Preheat oven to 350°F. Line a standard 12-cup muffin tin with baking cups.
Combine the flour, cornmeal, sugar, and baking powder in a bowl. Whisk to combine.
Combine oil, butter, and honey; stir in eggs and milk. Stir oil mixture into cornmeal mixture just until moistened. Do not overmix. Divide batter evenly among baking cups, filling each well up to the top.
Bake until tops are golden and a toothpick inserted into the centers comes out clean, about 18 minutes. Let cool for 10 minutes.