We build a novel equilibrium model in which households’ labor supply choices form the link between sorting on the marriage and sorting on the labor market. We first show that 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 explore how sorting patterns in each market amplify or mitigate the gender gap in wages, as well as income inequality between and within households. To this end, we estimate our model on German 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, on the evolution of inequality over time, and on spatial inequality differences between East and West Germany.