Family social capital can affect the interest and participation of parents in their children's education. The purpose of this study is to investigate the effect of family social capital on differences between and within families in the involvement of children's education. Considering the relationship between family members through the network configurations of family social capital, this study investigated the diversity of network types such as bonding or bridging of family structures in children's education, and the characteristics and effects of such diversity. This study used data from the Korean Children's Panel in 2015, when children entered elementary school. The sample of this study was confined to dual-income households. An operational definition of parental involvement in children's education was defined as educational enthusiasm. A parallel scale was applied to relax the group size limitation of parental data to utilize the advantages of multilevel analysis. Family social capital was classified into eight types that reflected the parent-child network types. The results of this study showed that there is no significant difference in family education enthusiasm between the fully connected type of family social capital and the open triad types. The triad types of family social capital has a significantly higher level of involvement in children’s education than the dyad types. The educational enthusiasm within the family is higher for mothers than for fathers, regardless of the types of family social capital. The mother-father educational disparity is minimal when fathers form a direct network with their children, while maximal when fathers and children are indirectly connected through mothers.