This paper relaxes the single-factor model of intergenerational educational mobility and analyzes heterogeneous effects of family background on children's education in villages, with a focus on the role of nonfarm occupations. The analysis uses data from rural China that cover three generations, and are not subject to coresident sample selection. Evidence from a battery of econometric approaches shows that the mean effects of parents' education miss substantial heterogeneity across farm-nonfarm occupations. Having nonfarm parents, in general, has positive effects, but children of low educated non-farmer parents (with higher income) do not enjoy any advantages over the children of more educated farmer parents. Estimates of cross-partial effects without imposing functional form show little evidence of complementarity between parental education and nonfarm occupation. The role of family background remains relatively stable across generations for girls, but for boys, family background has become more important after the market reform. The paper explores causality using three approaches: Rosenbaum sensitivity analysis, minimum biased inverse propensity weighted estimator, and heteroscedasticity-based identification. The analysis results suggest that the advantages of having more educated parents, especially with nonfarm occupations, are unlikely to be due solely to selection on genetic transmissions. However, the estimated positive effects of nonfarm over farmer parents among the low educated households may be driven entirely by moderate selection on genetic endowment.