Despite advances in areas such as the personalization of robots, sustaining adoption of robots for long-term use in families remains a challenge. Recent studies have identified integrating robots into families' routines and rituals as a promising approach to support long-term adoption. However, few studies explored the integration of robots into family routines and there is a gap in systematic measures to capture family preferences for robot integration. Building upon existing routine inventories, we developed Family-Robot Routines Inventory (FRRI), with 24 family routines and 24 child routine items, to capture parents' attitudes toward and expectations from the integration of robotic technology into their family routines. Using this inventory, we collected data from 150 parents through an online survey. Our analysis indicates that parents had varying perceptions for the utility of integrating robots into their routines. For example, parents found robot integration to be more helpful in children's individual routines, than to the collective routines of their families. We discuss the design implications of these preliminary findings, and how they may serve as a first step toward understanding the diverse challenges and demands of designing and integrating household robots for families.