In a large mixing bowl combine the sugar and butter until fluffy. Add eggs, milk, vanilla and lemon extract and mix until smooth. In a medium bowl, combine flours, baking powder, and salt.
Add dry ingredients to the wet in batches, stirring well. Drop soup spoonfuls of dough 2" apart on buttered baking sheets. Bake at 375* until edges begin to brown, 20-30 minutes.
Let cool completely. Put confections' sugar in a bowl. Stir in enough water to make the mixture thick and spreadable. Remove half the frosting to the top of a double boiler over simmering water.
Add chocolate and warm the mixture until chocolate is melted and the frosting is smooth. Remove from heat. With a brush, coat half the cookie with chocolate frosting and the other half with white frosting.