We consider a class of household production models characterized by a dichotomy property. In these models the amount of time spent on household production does not depend on the household utility function, conditional on household members having a paid job. We analyse the (non-parametric) identifiability of the production function and the so-called jointness function (a function describing which part of household production time is counted as pure leisure). It is shown that the models are identified in the two-adult case, but not in the single-adult case. We present an empirical application to Swedish time-allocation data. The estimates satisfy regularity conditions that were violated in previous studies and pass various specification tests. For this data set we find that male and female home production time are q-substitutes.