Preheat your oven to 400°F (200°C) and grease a 9x9 inch baking dish.
In a large bowl, whisk together the cornmeal, flour, sugar, baking powder, and salt.
In another bowl, mix the buttermilk, vegetable oil, and eggs until well combined.
Pour the wet ingredients into the dry ingredients and stir until just combined.
Fold in the diced jalapenos and shredded cheddar cheese.
Pour the batter into the prepared baking dish.
Bake for 25-30 minutes or until golden brown and a toothpick comes out clean.
Remove from the oven and let cool slightly before serving.
Cut into squares and serve warm with butter.
Enjoy your delicious jalapeno cornbread!