In a large saucepan, combine wheat berries and water; bring to a boil. Reduce heat; simmer, covered, 10 minutes. Stir in barley; simmer, covered, 5 minutes. Stir in rice; simmer, covered, 40-45 minutes or until grains are tender. Drain; transfer to a large bowl. Cool to room temperature.
Add apple, pomegranate seeds, green onions, carrot, celery and parsley to wheat berry mixture; toss to combine. In a small bowl, whisk dressing ingredients until blended. Pour over salad; toss to coat. Serve immediately or refrigerate and serve cold.