Preheat the waffle iron to a medium-high setting.
In a large mixing bowl, whisk together the cornmeal, all-purpose flour, baking powder, baking soda, and salt until uniform.
In a separate medium bowl, whisk together the buttermilk, beaten eggs, melted butter, and honey.
Incorporate the wet ingredients into the dry ingredients using a spatula, stirring until just combined to avoid over-developing gluten.
Fold the shredded cheddar cheese and diced jalapeños into the batter.
Lightly coat the waffle iron grids with non-stick cooking spray or melted butter.
Dispense approximately 0.5 to 0.75 cups of batter (depending on iron size) onto the center of the preheated grid.
Close the lid and cook for 4 to 5 minutes, or until the waffle is golden brown and the steam production has significantly subsided.
Remove carefully with a silicone spatula and repeat the process with the remaining batter.
Serve immediately to maintain the crispness of the exterior.