We propose a joint model to combine models for hospital visits and out-of-pocket medical expenditures. It allows for the presence of non-linear effects of covariates using splines to capture the effects of aging on healthcare demand. Sample heterogeneity is modeled robustly with the random effects following Dirichlet process priors with explicit cross-part correlation. We validate our model using a simulation study. We apply this model to Health and Retirement Survey data and show that healthcare varies with age and gender and exhibits significant cross-part correlation that provides a richer understanding of how aging affects healthcare demand.