We propose a model of intergenerational transmission of education wherein children belong to either highly educated or low-educated families. Children choose the intensity of their social activities while parents decide how much educational effort to exert. Using data on adolescents in the United States, we structurally estimate this model and find that, on average, children's homophily acts as a complement to the educational effort of highly educated parents but as a substitute for the educational effort of low-educated parents. We also perform some counterfactual policy simulations. We find that policies that subsidize kids' socialization efforts can backfire for low-educated students because they tend to increase their interactions with other low-educated students (i.e., homophily), which reduces the education effort of their parents and, thus, their chance of becoming educated. On the contrary, policies that increase heterophily by favoring friendship links between kids from different education backgrounds can be effective in reducing the education gap between them.