Pré-publication, Document de travail: We use an overlapping generations model to investigate the role of parental health investment and children's schooling on the aggregate level of human capital and inequality. In our model, parental longevity affects children's human capital since it impacts human capital transmission. When poor parents cannot afford to invest in health, poverty traps may arise as human capital levels remain low in the long run. Both health costs and public school quality are crucial in determining whether households fall into the poverty trap. We demonstrate that high-quality schools ensure that successive generations become more educated, eventually attaining a higher human capital steady state. However, public health investments are particularly effective, as they affect household income and schooling and allow for human capital transmission through generations. We calibrate our model for Brazil and Chile and show that our model predicts that a poverty trap will arise in Brazil but not in Chile.