Background Numerous studies suggest that interpersonal relationships and social support influence the development of postpartum depression and sleep quality for women. However, the effect of support from the husband or the mother-in-law has not been thoroughly validated. The current study examined the relative contribution of marital satisfaction, perceived caring of the mother-in-law, and social support on postpartum depression and sleep quality simultaneously in a path model. Methods A cross-sectional study was conducted from March to June 2017 in Hebei, China, using a self-report questionnaire. A total of 817 women participated at 6 weeks postpartum. Sociodemographics and information about marital satisfaction, perceived caring of the mother-in-law, social support, postpartum depression, and sleep were collected. Path analysis was used to analyze the cross-sectional data. Results The final model had a highly satisfactory fit. Marital satisfaction and perceived caring of mother-in-law had both direct and indirect effects on postpartum depression through social support, but these two variables had only an indirect effect on sleep quality through social support and postpartum depression. Sleep quality is a consequence of postpartum depression at 6 weeks after delivery. The prevalence of minor and major postpartum depressive symptoms at 6 weeks postpartum was 41.49 and 23.13%, respectively. A total of 371 (45.41%) women experienced sleep disturbance at 6 weeks postpartum. Conclusions These findings suggest that interpersonal relationships with family members play important roles in postpartum depression and sleep quality through social support in Chinese women. Improving the relationship between new mothers and their husbands or mothers-in-law and then enhancing social support might reduce postpartum depression and sleep disturbance.