Preheat your oven to 375°F (190°C). Grease a 9-inch square baking pan and set aside.
In a medium bowl, whisk together the cornmeal, flour, sugar, baking powder, baking soda, and salt.
In a separate large bowl, combine the buttermilk, melted butter, and eggs. Mix until well combined.
Gradually add the dry ingredients to the wet ingredients, stirring until just combined.
Gently fold in the chopped jalapeños.
Pour the batter into the prepared baking pan and spread it evenly.
Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
While the cornbread is baking, prepare the lime honey glaze by combining the honey, lime juice, and lime zest in a small saucepan over low heat. Stir until warm and well combined.
Once the cornbread is done baking, remove it from the oven and let it cool for a few minutes.
Brush the lime honey glaze over the warm cornbread. Allow it to soak in slightly before slicing and serving.