In large bowl, mix together cheeses, chicken, onion, olives, sour cream, parsley and pepper and set aside.
In a sauté pan, heat butter over low heat. Add flour and cook for a few minutes, stirring constantly. Stir in milk and 1/2 cup chicken broth. Bring to a boil; while stirring, boil for 1 minute.
Add remaining chicken broth, cook and stir until hot and thickened, add spinach, sour cream, green chilies, onion, garlic and cumin.
Dip each tortilla into sauce, coating both sides. Spoon about 1/2 cup filling into each tortilla and roll up. Place seam-side down in an ungreased 9 x 13" baking dish. Pour remaining sauce over enchiladas and bake uncovered in a 350° oven about 20 minutes until bubbly. Garnish with shredded cheese, lime and tomato slices.