Preheat oven to 350*F. Grease, spray, or line muffin tins (makes about 18).
In a medium bowl, mix together flours, baking powder, salt, baking soda, cinnamon, and cloves.
In a separate large bowl, cream together butter, white sugar, and brown sugar. Beat in eggs. Add half of the flour mixture, mix until just combined, then add half of the cider, mix until just combined. Repeat with the rest of the flour and cider.
In another small bowl, mix together chopped apples with lemon juice. Fold these into the batter.
Scoop into muffin tins and bake for 20-25 minutes or until a toothpick inserted in the center comers out clean. Cool completely on a wire rack before removing from muffin tins.
If you prefer, shred the apples instead of chopping them for less visible pieces of apple.
Top the muffins with a cinnamon sugar mixture before baking. Or glaze the muffins after baking with a glaze made of powdered sugar and apple cider.