Joint modeling of multiple health related random variables is essential to develop an understanding for the public health consequences of an aging population. This is particularly true for patients suffering from multiple chronic diseases. The contribution is to introduce a novel model for multivariate data where some response variables are discrete and some are continuous. It is based on pair copula constructions (PCCs) and has two major advantages over existing methodology. First, expressing the joint dependence structure in terms of bivariate copulas leads to a computationally advantageous expression for the likelihood function. This makes maximum likelihood estimation feasible for large multidimensional data sets. Second, different and possibly asymmetric bivariate (conditional) marginal distributions are allowed which is necessary to accurately describe the limiting behavior of conditional distributions for mixed discrete and continuous responses. The advantages and the favorable predictive performance of the model are demonstrated using data from the Second Longitudinal Study of Aging (LSOA II).