Preheat the oven to 425 degrees F and place a 6.5-inch cast iron skillet inside to heat while you make the batter.
In a medium size bowl, whisk together the cornmeal, flour, sugar, salt, baking powder, and baking soda. Whisk in the milk, buttermilk, and egg. Whisk in almost all of the melted butter, reserving about 1/2 tablespoon for the skillet later on.
Carefully remove the hot skillet from the oven. Reduce oven temperature to 375 degrees F.
Add the reserved butter to the hot skillet. Pour the batter into the skillet (it should sizzle and butter should pool around it) and place it in the center of the oven. Bake until the center is firm and a cake tester or toothpick inserted into the center comes out clean, 20 minutes. Allow to cool for 10 to 15 minutes and serve.
Note: I've never had the cornbread spill over, as it tends to bake around the sides first and rise up. However, if you are worried about it you can put a rimmed baking sheet on the lower rack to catch any drips.