In a large bowl, combine the green and red cabbages; set aside. In a medium bowl, whisk together the mayonnaise, sour cream, vinegar, celery seed, salt, and pepper. Add the apple slices.
Pour over the cabbage and toss gently until coated. Cover and chill 1 hour or longer. To serve, spoon into salad bowls and sprinkle with the parsley (if desired).