Beat Neufchatel cheese, mayonnaise, Cheddar cheese, jalapeno pepper, and green chiles together in a large bowl until evenly mixed; spread into a 2-quart casserole dish. Sprinkle Parmesan cheese over the top of the mixture; top with bread crumbs.
Bake in preheated oven until lightly browned around the edges, 25 to 30 minutes.
