Gather all ingredients.
Preheat the oven to 350 degrees F (175 degrees C). Lightly grease a 9x13-inch casserole dish.
Bring a large pot of lightly salted water to a boil. Cook egg noodles in boiling water, stirring occasionally, until tender yet firm to the bite, 7 to 9 minutes. Drain and transfer noodles to the prepared casserole dish.
Top noodles with chicken, ham, and Swiss cheese.
Mix together condensed soup, milk, and sour cream in a medium bowl until combined; spoon over noodle mixture in the casserole dish.
Melt butter in a skillet over medium heat; cook and stir bread crumbs and Parmesan cheese in hot butter until crumbs are well coated, 2 to 3 minutes. Sprinkle over casserole.
Bake in the preheated oven until casserole is bubbling and lightly browned, about 30 minutes.
Allow to cool slightly before serving.
