Place a rack in the middle of the oven and preheat the oven to 350 degrees F. Line a 9-by-13-inch baking pan with aluminum foil and spray foil with pan spray.
Stir together cornmeal, all-purpose flour, cake flour, sugar, baking powder, and salt. Set aside.
In a medium bowl, whisk together eggs. Melt butter and immediately whisk into eggs in a slow stream. Whisk in oil, milk, and buttermilk. Whisk in dry ingredients just until combined.
Scrape batter into the pan and bake for 30 minutes. Rotate pan from front to back and continue to bake for 5 to 10 more minutes, or until a tester inserted in the center comes out clean.
To make the glaze: While corn bread is baking, melt butter in a medium saucepan. Add honey and water and whisk until blended. When corn bread is done, remove from oven and poke holes all over the bread, about 1/2 inch apart, with a toothpick. Brush with the glaze and allow to cool. Store at room temperature in an airtight container.