Preheat oven to 400 degrees F. Grease a 9-inch square baking pan.
In a medium bowl, combine cornmeal, flour, sugar, baking powder, salt, baking soda, and jalapeños; set aside.
In another bowl, whisk together the eggs, buttermilk and oil. Add to the dry ingredients and stir just until moistened. Stir in cheese. Pour into a greased 9-in. square baking pan.
Bake 20-22 minutes or until a toothpick inserted in the center comes out clean. Cut into squares or wedges. Serve warm.