Cut cabbage and carrots into very small pieces (about the size of rice kernels is about right). Place in a large bowl and mix together.
In a bowl combine the sugar, salt, pepper, milk, mayonnaise, buttermilk, vinegar and lemon juice. Beat until it is smooth. Pour over the cabbage and carrots. Mix well. Cover and refrigerate for at least 2 hours before serving to allow the flavors to mix.