Preheat oven to 450 degrees F. Line a cookie sheet with non-stick foil or parchment paper.
Mix the flours, sugar, baking powder, salt and baking soda in large bowl. Add cream cheese and butter and work the fat into the flour with your fingers until you get a crumbly mixture. Add the buttermilk and stir with a spoon until mixture comes together.
Turn the dough out onto a floured board and push it all together to make a 4x6 inch rectangle. Cut into 6 squares and put biscuits on baking sheet. Bake on center rack for 12 to 15 minutes or until they have puffed and are golden brown. As soon as they come out of the oven, brush the tops with butter. As delicious as these biscuits were with the cream cheese, they really did benefit from the extra finish of butter on the top.