Background: Existing research has examined the link between family health and mental health outcomes like depression and anxiety, but the mechanisms are unclear. Sleep quality may play a mediating role, and the effects of family health on mental health can differ based on living arrangements, which influence experiences and social support. This study aimed to investigate the mediating role of sleep quality in the relationship between family health and depression or anxiety across diverse living statuses. Methods: This cross-sectional study was conducted from June to September 2023 in five regions of China, including Guangdong Province, Guangxi Province, Jiangsu Province, Sichuan Province, and Macao Special Administrative Region. Family health was assessed using the Short Form of the Family Health Scale, while sleep quality was measured using the Self-Rating Scale of Sleep. Depression and anxiety were evaluated using the Hospital Anxiety and Depression Scale. Mediation analysis was conducted to examine the mediating effect of sleep quality on the relationship between family health and mental health outcomes. Subgroup analyses were conducted to explore potential variations in the mediating role of sleep quality across different living status. Results: This study sample comprised 4918 participants, with a mean age of 30.1 years (SD = 12.6). The direct effect analysis demonstrated a significant negative correlation between family health and symptoms of depression (β = −0.216, p < 0.001) or anxiety (β = −0.199, p < 0.001). The mediation analysis results revealed that family health had a significant indirect effect on symptoms of depression (β = −0.040, p < 0.001) or anxiety (β = −0.050, p < 0.001) through sleep quality. Specifically, both the living with family group and the living in a shared accommodation group showed a significant mediation effect of sleep quality in the relationship between family health and mental health outcomes. However, the living alone group did not show a significant mediation role. Conclusions: Sleep quality mediated the relationship between family health and symptoms of depression or anxiety, with significant effects in those living with family or in shared accommodations, but not those living alone. These findings underscore the importance of considering living status when examining mental health outcomes and developing interventions.