Abstract We develop a new equilibrium model in which households’ labour supply choices form the link between sorting on the marriage market and sorting on the labour market. We first show that in theory, the nature of home production—whether partners’ hours are complements or substitutes—shapes equilibrium labour supply as well as marriage and labour market sorting. We then estimate our model using German data to empirically assess the nature of home production, and find that spouses’ home hours are complements. We investigate to what extent complementarity in home hours drives sorting and inequality. We find that home production complementarity strengthens positive marriage sorting and reduces the gender gap in hours and in labour sorting. This puts significant downward pressure on the gender wage gap and on within-household income inequality, but fuels between-household inequality. Our estimated model sheds new light on the sources of inequality in today’s Germany, and—by identifying important shifts in home production technology toward more complementarity—on the evolution of inequality over time.