Preheat oven to 350°.
Coat a 9-inch cast-iron skillet with oil. Place in oven for 10 minutes.
Lightly spoon flour and masa harina into dry measuring cups; level with a knife. Combine flour, masa harina, cornmeal, baking powder, and salt in a large bowl, stirring well with a whisk.
Combine water and remaining ingredients in a small bowl, stirring with a whisk. Add water mixture to flour mixture, stirring until moist. Spoon batter into preheated pan.
Bake at 350° for 25 minutes or until a wooden pick inserted in center comes out clean. Remove corn bread from pan; cool completely on a wire rack.