Preheat your oven to 350°F (175°C) and grease a baking dish.
Cook the diced chicken in a skillet over medium heat until no longer pink.
Add diced ham to the skillet and cook for an additional 2-3 minutes.
In a large bowl, combine shredded Swiss and mozzarella cheeses.
In another bowl, mix sour cream, mayonnaise, and Dijon mustard.
Layer half of the chicken and ham mixture in the baking dish.
Spread half of the cheese mixture over the chicken and ham.
Repeat the layers with the remaining chicken, ham, and cheese mixture.
Top with breadcrumbs mixed with melted butter.
Bake for 45 minutes until golden and bubbly.