For family studies, there is now an established analytical framework for binary-trait outcomes within the generalized linear mixed models (GLMMs). However, the corresponding analysis of multivariate binary-trait (MBT) outcomes is still limited. Certain diseases, such as schizophrenia and bipolar disorder, have similarities in epidemiological features, risk factor patterns and intermediate phenotypes. To have a better etiological understanding, it is important to investigate the common genetic and environmental factors driving the comorbidity of the diseases. In this paper, we develop a suitable GLMM for MBT outcomes from extended families, such as nuclear, paternal- and maternal-halfsib families. We motivate our problem with real questions from psychiatric epidemiology and demonstrate how different substantive issues of comorbidity between two diseases can be put into the analytical framework.