This study contributes to the literature on how parenthood affects the within-couple gender earnings gap. It examines how this 'child penalty' on women's earnings varies with the education level of both partners and the woman's relative education within the couple. Using Austrian register data on 268,156 heterosexual couples who entered parenthood between 1990 and 2007, and an event study design that uses the couple as the unit of analysis, we examine the heterogeneity in the magnitude of the child penalty. Our stratified analyses show that the average child penalty is smaller for women in hypogamous couples, where she is more educated than her partner, than for women in homogamous or hypergamous unions, where the male partner is equally or less educated. These results are confirmed by multivariate regressions that control for compositional effects and disentangle the effects of partners' level of education from the impact of the woman's relative education within the couple. Furthermore, examining detailed educational pairings, rather than lumping couples into three broad types, reveals a larger variation in the size of the child penalty: tertiary-educated women in hypogamous unions incur substantially smaller penalties compared to all other educational pairings, while women in hypergamous unions with a tertiary-educated man face particularly large penalties. Supplementary analyses suggest that the reduced child penalties for tertiary-educated women in hypogamous unions do not reflect a selection of men with low earning potential into this union type.