Preheat oven to 350°F Drain and seed the green chiles before mincing them. Set them aside while you make the cornbread batter.
Beat the eggs with the milk. Sift the cornmeal, soda, and salt together into a large mixing bowl. Quickly stir the liquid ingredients into the cornmeal. Use as few strokes as possible to mix in the canned corn and melted butter.
Pour half of the butter into an oiled 1 1/2-quart casserole dish. Sprinkle all of the chiles and half of the cheese over the batter. Pour the rest of the batter over them and top with the remaining cheese.