In a medium bowl, stir together the artichokes, mayonnaise, sour cream, mozzarella cheese, onion, Parmesan cheese, and green chiles. Season with salt and pepper, adjusting the amounts to taste. Sprinkle lightly with cayenne pepper.
Transfer to a 2-quart baking dish then bake for 25 minutes, or until lightly golden and bubbly. Let the dip stand for at least 15 minutes to set then serve hot.