Preheat oven to 375 degrees F.
In separate bowls, mix together the chicken filling ingredients and the beef filling ingredients. Season each with salt and pepper. Set aside.
In a small bowl, stir enchilada sauce with sour cream or heavy cream if using.
Spread a thin layer of enchilada sauce on the bottom of a 9x13 baking dish.
Warm tortillas in the microwave 20 seconds to make them pliable. Fill each tortilla with 2 to 3 tablespoons of filling, roll tightly, and place seam-side down. Keep chicken enchiladas on one side of the dish and beef on the other for easy serving.
Pour remaining enchilada sauce evenly over all enchiladas. Sprinkle shredded cheese over the top.
Cover with foil and bake 20 minutes. Remove foil and bake an additional 10 minutes until cheese is melted and bubbling.
Rest 5 minutes before serving. Garnish with cilantro if desired.