We build a novel equilibrium model in which households' labor supply choices form the link between sorting on the marriage market and sorting on the labor market. We first show that in theory, the nature of home production – whether partners' hours are complements or substitutes – shapes marriage market sorting, labor market sorting and labor supply choices in equilibrium. We then estimate our model on German data to assess the nature of home production in the data, and find that spouses' home hours are complements. We investigate to what extent complementarity in home hours drives sorting and inequality. We find that the home production complementarity – by strengthening positive marriage sorting and reducing the gender gap in hours and labor sorting – puts significant downward pressure on the gender wage gap and within-household income inequality, but it 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 towards more complementarity – on the evolution of inequality over time.