Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the shredded chicken, diced ham, and Swiss cheese. Mix well and set aside.
In another bowl, whisk together the milk, mayonnaise, Dijon mustard, garlic powder, black pepper, and salt until smooth.
Pour the milk mixture over the chicken and ham mixture, stirring until everything is evenly coated.
Transfer the mixture to a greased 9x13 inch baking dish, spreading it out evenly.
Sprinkle the breadcrumbs evenly over the top of the casserole.
Bake in the preheated oven for 30-35 minutes, or until the top is golden brown and the casserole is bubbly.
Remove from the oven and let it cool for about 5 minutes before serving. Garnish with fresh parsley if desired.