For the muffins: Preheat the oven to 425 degrees F. Prepare a muffin tin with cooking spray.
Stir together the cornmeal, flour, baking powder, baking soda and salt in a large bowl.
Add the buttermilk and eggs to a small pitcher and stir to combine. Pour the buttermilk mixture into the dry ingredients. Stir with a fork until combined. Fold in the cheese, green chiles and melted butter until just combined.
Portion the batter into the prepared muffin tin and bake until they are cooked through, about 15 minutes.
For the honey butter: Mix the butter and honey in a bowl until combined. Transfer to a ramekin. Remove the muffins from the oven, allow to cool a little, then break open and spread with the honey butter.