Preheat the oven to 350˚F. Line a baking sheet with foil or parchment paper.
Slice each jalapeño down the center, and remove seeds and ribs. Try to keep some stem on each half.
In a medium bowl, combine flour, cornmeal, sugar, salt, oil, and milk until just mixed. Stir in 1/2 cup of the cheese and all of the corn. Carefully spoon the batter into each jalapeño half until barely mounded. Sprinkle with the remaining cheddar.
Bake for about 20 minutes, or until the cornbread is firm and cooked through. At sea level, the baking time should be closer to 15 minutes.