Preheat your oven to 400°F (200°C). Grease a baking dish.
In a large mixing bowl, combine the cornmeal, flour, baking powder, salt, and baking soda.
In another bowl, whisk together the buttermilk, eggs, and melted butter.
Pour the wet ingredients into the dry ingredients and stir until just combined.
Fold in the corn kernels, cheddar cheese, and green chilies.
Pour the batter into the prepared baking dish and spread it out evenly.
Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Let cool slightly before serving. Enjoy!