In a medium bowl, stir butter, sugar and honey together. Whisk in eggs and buttermilk. Add cornmeal, flour, salt and baking soda. Do not over-mix. As soon as the flour disappears, stop mixing. Fold in jalapeno and cheese.
Divide batter equally between the cups of a greased or lined muffin tin, filling almost to the top. Bake for 25 minutes. Prick the center of one muffin with a toothpick and make sure it comes out clean. If not clean, bake for about 5 more minutes.
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