In a ceramic or glass bowl combine crab, onions, tomato and parsley. In a cup or bowl combine juices and stir into crab mixture. Season with salt and pepper. Cover and chill in refrigerator overnight or for at least 6-8 hours.
Combine cream cheese and mayonnaise, blending. Spread over the bottom of a round platter or serving plate. Spread the avocado as the next layer. Remove the crab mixture from the refrigerator and drain so that all of the moisture is removed (or at least close). Spread on top of the avocado. Sprinkle with minced fresh parsley and serve with tortilla chips.