This study reveals substantial heterogeneity in how mothers and fathers responded to COVID-19-related school closures in Russia. Employing the correlated random coefficient model with individual fixed effects across a 6-year panel, we find that, on average, school closures did not impact working hours but resulted in decreased employment and increased remote work, with the effect on mothers being notably more pronounced than on fathers. However, the variation in treatment effects is striking across parental, children’s, and household characteristics, and regional conditions. In several subsamples, the employment response of fathers closely mirrors that of mothers, especially among older parents, those with younger pre-school children, and in regions with low unemployment rates. When interacting with two or more different factors, the study unveils a complex within-family production function determining the differential responses of parents under diverse regional, temporal and family circumstances.