Preheat the oven to 375°F and place a 10-inch skillet inside.
Whisk together dry ingredients (cornmeal, flour, sugar, baking powder, salt, and baking soda).
In another bowl, mix wet ingredients (buttermilk, eggs, melted butter).
Add wet ingredients to dry, stirring until just combined.
Stir in cheese and jalapeños. Add milk if the batter is too thick.
Remove the skillet from the oven, grease with butter, and pour in the batter.
Bake for 20-25 minutes until golden and cooked through.
Slice and serve warm.