Preheat oven to 400°F (200°C). Grease a 9-inch square baking dish.
In a large bowl, combine cornmeal, flour, sugar, baking powder, and salt.
In another bowl, whisk together milk, eggs, and vegetable oil.
Add the wet ingredients to the dry ingredients and stir until combined.
Fold in the corn, green chilies, and cheddar cheese.
Pour the batter into the prepared baking dish.
Bake for 30 minutes, or until a toothpick inserted into the center comes out clean.
Let cool slightly before serving.