Preheat oven to 350 degrees. Line a standard 12-cup muffin tin with baking cups. Whisk together cornmeal, flour, sugar, baking powder, and 1 1/4 teaspoons salt in a large bowl. Combine oil, butter, and honey; stir in eggs and milk. Stir oil mixture into cornmeal mixture. Divide batter evenly among baking cups.
Bake until tops are golden and a toothpick inserted into the centers comes out clean, about 18 minutes. Let cool for 10 minutes.
Muffins can be stored at room temperature for up to 4 days.
This recipe could also make 24 mini muffins. Bake them for about 15 minutes.