Preheat oven to 400° and grease a 9 x 9" baking dish. Line bottom of the dish with parchment paper with 3" extensions on end for lift.
Beat butter and granulated sugar together in a large bowl until smooth.
In a separate bowl, combine cornmeal, flour, baking powder, and salt.
In a third bowl stir together buttermilk, honey, and eggs.
Add ½ of the milk mixture, then ½ of the dry mixture into the sugar/butter mixture, whisking after each addition. Repeat with the rest of the ingredients. Stir in the jalapenos.
Spread mixture evenly into the prepared baking dish. Bake in the preheated oven for approximately 25 minutes. If a toothpick inserted in the middle does not come out clean, cover the cornbread with aluminium foil and bake for an additional 10 - 15 minutes as needed. Let cool on a wire rack for about 20 minutes before slicing.
You can use a 9x13 pan but it will produce a thinner bread. The cooking time for the larger pan will be 17 - 20 minutes at 400 degrees.