The evolution of parent-offspring interactions for the provisioning of care is usually explained as the phenotypic outcome of resolved conflicting selection pressures. However, parental care and offspring solicitation are expected to have complex patterns of inheritance. Here we present a quantitative genetic model of parent-offspring interactions that allows us to investigate the evolutionary maintenance of a state of resolved conflict. We show that offspring solicitation and parental provisioning are expected to become genetically correlated through coadaptation and that their genetic architecture is dictated by an interaction between patterns of selection and the proximate mechanisms regulating supply and demand. When selection is predominately on offspring solicitation, our model suggests that the genetic correlations between provisioning and solicitation are usually positive if provisioning reduces solicitation. Conversely, when selection is predominately on parental provisioning, the correlations are mostly negative as long as parents show a positive response to offspring demand. Empirical estimates of the genetic architecture of traits involved in family interactions fit these predictions. Our model demonstrates how the evolutionary maintenance of parent-offspring interactions can result in variable patterns of coadaptation, and it provides an explanation for the diversity of family interactions within and among species.