In families composed of parents and children, the health of parents and children is often interrelated: the health of children can have an impact on the health of parents, and vice versa. However, the design of health tracking technologies typically focuses on individual self-tracking and self-management, not yet addressing family health in a unified way. To examine opportunities for family-centered health informatics, we interviewed 14 typically healthy families, interviewed 10 families with a child with a chronic condition, and conducted three participatory design sessions with children aged 7 to 11. Although we identified similarities between family-centered tracking and personal self-tracking, we also found families want to: (1) identify ripple effects between family members;(2) consider both caregivers and children as trackers to support distributing the burdens of tracking across family members; and (3) identify and pursue health guidelines that consider the state of their family (e.g., specific health guidelines for families that include a child with a chronic condition). We contribute to expanding the design lens from self-tracking to family-centered health tracking.