There has been considerable interest, and consequent progress, in the modeling of household vehicle fleet composition and utilization in the travel behavior research domain. The multiple discrete-continuous extreme value (MI)(EV) model is a modeling approach that has been applied frequently to characterize this choice behavior. One key drawback of the MDCKV modeling methodology is that it does not provide an estimate of the count of vehicles in each vehicle type alternative represented in the MDCKV model. Moreover, the classic limitations of the multinomial logit model, such as violations of the independence of irrelevant alternatives property in the presence of correlated alternatives and the inability to account for random taste variations, apply to the MDCKV model as well. A new methodological approach, developed to overcome these limitations, is applied in this paper to model vehicle fleet composition and count in each body type. The modeling methodology involves tying together a multiple discrete-continuous probit (MDCP) model and a multivariate count (MC) model capahle of estimating vehicle counts in vehicle type categories considered by the MDCP model. The joint MDCP-MC model system was estimated by using a Greater Phoenix, Arizona, travel survey data set. The joint model system was found to oiler behaviorally intuitive results and to provide superior goodness of fit in comparison with an independent model system that ignores the jointness between the MDCP component and the MC component.