Combine the cornmeal, flour, baking soda, salt and garlic powder in a bowl. Mix well and set aside.
Melt the butter in a large pan or cast-iron skillet over medium-high heat. Transfer the melted butter to a medium bowl, add the buttermilk, milk, honey and eggs and whisk until blended. Stir in the jalapenos, green onions and 1/2 cup of the Cheddar. Add the cornmeal mixture and beat until very few lumps remain.
Pour the batter into the hot skillet and bake for 25 minutes. Sprinkle the cornbread with the remaining 1 cup Cheddar and continue to bake until a toothpick inserted in the center comes out clean, another 10 to 15 minutes. Transfer to a wire cooling rack and allow to cool before slicing.