Preheat oven to 375. Grease an 8x8 pan and set aside.
In a medium bowl, combine brown sugar, white sugar, and melted butter and mix well. Add eggs and stir together until fully combined. Add milk and stir again.
In a separate bowl, combine flour, cornmeal, baking soda, and salt.
Add wet ingredients to dry ingredients, and stir until just combined.
Pour batter into grease pan, and bake at 375 for 25-30 minutes, or until toothpick inserted comes out clean.