Start by finely chopping the green cabbage and carrots. A food processor can make this task easier.
In a separate bowl, whisk together the mayonnaise, buttermilk, milk, distilled white vinegar, lemon juice, granulated sugar, salt, and ground black pepper until well combined.
In your large mixing bowl, add the chopped cabbage and carrots. Pour the dressing over the vegetables and gently mix until everything is well coated.
Cover the bowl with plastic wrap or transfer to a storage container. Refrigerate for at least 1-2 hours before serving.
Once chilled, give the coleslaw a quick stir and serve it alongside your favorite dishes.