Whisk the vinegar, mustard, lemon juice, garlic, olive oil, salt, and pepper in small bowl to blend.
Combine the vinaigrette and chicken pieces in a large resealable plastic bag; seal the bag and toss to coat.
Refrigerate, turning the chicken pieces occasionally, for at least 2 hours and up to 1 day.
Preheat the oven to 400 degrees F. Remove chicken from the bag and arrange the chicken pieces on a large greased baking dish. Roast until the chicken is just cooked through, about 1 hour. If your chicken browns too quickly, cover it with foil for the remaining cooking time.
Transfer the chicken to a serving platter. Place the baking dish on a burner over medium-low heat. Whisk the chicken broth into the pan drippings, scraping up any browned bits on the bottom of the baking sheet with a wooden spoon and mixing them into the broth and pan drippings. Drizzle the pan drippings over the chicken. Sprinkle the lemon zest and parsley over the chicken, and serve.