We develop a method for distributional regression of joint multidimensional choice on nonlinear prices departing from a household model of labor supply that focuses on tax policy effects. Our distribution functions are derived under minimal theoretical assumptions and have a simple structure. We allow distribution-free estimation, collective decisionmaking, and identification based on tax reforms. In our empirical application on U.S. panel data from 1980 to 2006, we provide a deepened understanding of how the configuration of the tax system affects the distribution of transitions between combinations of spouse labor supply. We also quantify biases from commonly imposed restrictions.