Preheat oven to 350°F (175°C).

Grease a 9-inch square baking pan.

In a large bowl, combine cream-style corn, buttermilk, vegetable oil, and beaten eggs.

Mix the ingredients well until combined.

Stir in the cornbread mix until just combined, being careful not to overmix.

Drain the canned green chilies thoroughly.

Pour half of the cornbread batter into the greased baking pan.

Sprinkle the drained green chilies evenly over the batter in the pan.

Sprinkle half of the shredded cheddar cheese evenly over the green chilies.

Pour the remaining cornbread batter over the cheese and chilies.

Sprinkle the remaining cheddar cheese evenly over the top of the batter.

Bake in the preheated oven for 45 to 50 minutes, or until a wooden skewer inserted into the center comes out clean.

Let the cornbread cool slightly in the pan before cutting into squares.

Serve warm.