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