Combine mayonnaise, milk, buttermilk, sugar, vinegars, lemon juice, salt and pepper in a large bowl. Whisk well until the sugar is dissolved.
Add cabbage, carrot and onion, and toss well. Be sure cabbage, carrot and onion are chopped into very small pieces, about the size of rice. Cover and chill for at least two hours before serving. Overnight is even better.