Combine the cornmeal, flour, sugar, baking powder, baking soda, and salt in a bowl. Whisk together the egg, milk, and butter in another bowl. When everything is well-combined, pour the dry ingredients into the wet ingredients. Fold in the chiles, corn, onion, and cheese. Mix just until combined.
Oil an 8-inch cast-iron skillet or an 8 x 8-inch baking pan and pour in cornbread mixture.
Cook for 20-25 minutes, until the edges are golden and the middle is fully cooked.