In a large bowl, whisk together the mayonnaise and orange juice. Add ham, red apples, yellow apples and celery and toss until thoroughly coated, to ensure that the apples do not brown. Chill 4 hours or overnight.
Just before serving, toss in parsley. Serve on a bed of lettuce. NOTE: You may also add 1/2 cup halved seedless grapes, raisins, sunflower seeds or walnut halves.