Place oven rack in middle position and heat oven to 400 degrees
Grease light-colored 9-inch round or 8-inch square baking pan and line with parchment paper
In a large bowl, whisk together cornmeal, flour, sugar, baking powder, baking soda, and salt
In a medium bowl, whisk together milk, eggs, and melted butter
Stir milk mixture into cornmeal mixture mixing until just incorporated
Stir in the minced jalapeños and 1 cup of the cheese
Add batter to prepared pan and sprinkle top with remaining 1/2 cup of cheese
Bake for about 30 minutes until light golden brown and a toothpick inserted in the middle comes out clean, rotating pan halfway through baking
Cool pan on a wire rack for 10 minutes, then remove cornbread from pan and allow to cool 20 minutes longer