The purpose of this study was to investigate whether the well-being of caregivers is mediated by the association between behavioral and psychological symptoms in elderly relatives and the quality of sleep experienced by caregivers using a mediational model. The participants were 105 working family caregivers in Japan. We assessed well-being based on the Kessler Scale 10, self-rated health, and satisfaction in daily life. Our results showed that the well-being in working family caregivers was impacted by the severity of behavioral and psychological symptoms in elderly relatives. Well-being in working family caregivers was also affected by quality of sleep. Maintaining good quality of sleep in working family caregivers is important for reducing caregiver burden and psychological distress, and for improving the balance between work and family life.