Preheat oven to 350 degrees. Grease an 8" square baking pan.
In a large bowl, combine the flour, cornmeal, sugar, baking powder, salt and baking soda.
In a separate bowl, combine the eggs, buttermilk and milk; mix well.
Add the wet mixture to the dry mixture and stir until just combined. Stir in the butter.
Pour batter into the prepared pan and bake for 30-35 minutes or until a wooden skewer inserted into the center comes out clean. Let cornbread cool slightly before serving.
Notes
I rarely buy buttermilk because it's so easy to make with ingredients you likely have on hand. Just pour 1 tablespoon lemon juice or white vinegar in a measuring cup and add enough milk to hit the 1-cup line. Let the mixture sit at room temperature for 5-10 minutes until curdled.
Recipe by Two of a Kind at http://www.twoofakindcooks.com/quick-easy-cornbread/