Preheat oven to 350°F with oven rack positioned 8 inches from heat source. Place squash and brussels sprouts on a large rimmed baking sheet; drizzle with oil, and toss to coat. Pat chicken dry. Arrange chicken, skin side up, and vegetables in a single layer on baking sheet. Sprinkle evenly with coriander and 1/2 teaspoon each of the salt and pepper.
Bake in preheated oven until a thermometer inserted in thickest portion of chicken registers 140°F, 25 to 30 minutes. Increase oven temperature to broil (do not remove baking sheet from oven); broil until chicken reaches 165°F and vegetables are tender and browned, about 7 minutes. Remove from oven; sprinkle chicken and vegetables evenly with remaining 1/4 teaspoon salt. Let chicken rest 5to 10 minutes.
Meanwhile, whisk together mayonnaise, milk, chives, water, juice, and remaining 1/4 teaspoon pepper in a small bowl.
To serve, drizzle chicken and vegetables with mayonnaise sauce; sprinkle with pomegranate seeds and parsley.