Preheat oven to 400 degrees. Grease a 3-quart baking dish.
In a large bowl whisk together the cornmeal, flour, salt, baking powder, and baking soda.
In a separate bowl, beat the softened butter and sugar. Beat the sour cream and eggs into the butter-sugar mixture.
Add the milk and the dry ingredients, a third at a time, and alternating wet/dry.
Mix in the green chiles, corn, and shredded cheese. Pour mixture into prepared baking dish.
Bake at 400°F for 35 minutes, or until top is browned, the center springs back when pressed down, and a skewer inserted into the center comes out clean.
Let cool almost completely before serving.