Preheat your oven to 400°F (200°C).
Grease a 9-inch round or square baking pan.
In a large bowl, whisk together cornmeal, flour, sugar, baking powder, and salt.
In another bowl, mix buttermilk, eggs, and melted butter until well combined.
Pour the wet ingredients into the dry ingredients, stirring until just combined.
Fold in the diced jalapenos and shredded cheese.
Pour the batter into the prepared baking pan.
Bake for 25-30 minutes or until a toothpick inserted in the center comes out clean.
Allow the cornbread to cool for a few minutes before slicing.
Serve warm and enjoy!