This study investigates the relationships between family composition measures (i.e. parental separation and sibship size) and higher education attainment across cohorts, countries, and regions, and by parental education levels contrasting them with intergenerational education attainment. Using the Generation and Gender Survey, with 18 countries, 226 regions, and 107,185 individuals, and employing multilevel fixed-effect models, we explore the variation in the association between family composition measures and higher education attainment, as well as the average association based on parental education levels. The variation in the association between family composition measures and educational attainment is considerably smaller compared to the strength of intergenerational transmission of education both within and between countries and across the cohorts. Changes in parental education level are associated with the changes across generations in the association between the sibship size and educational attainment. The average association between parental divorce and educational attainment is similar across place, generation and family of origin. Country-specific institutions exert a greater influence on intergenerational educational transmission than on the effects of family composition on educational attainment.