Combine rice, cream of chicken soup, and cream of mushroom soup in a large bowl. Mix in vegetables, shredded chicken, 1 cup Mexican cheese blend, and salsa. Transfer chicken mixture to a baking pan. Sprinkle remaining cheese evenly on top.
Melt margarine in a skillet over medium heat. Add bread crumbs, stirring constantly until the crumbs turn golden brown, about 5 minutes. Pour bread crumbs evenly over the chicken mixture.
Bake in the preheated oven until heated through, about 45 minutes.