In the current paper, we propose a new utility-consistent modeling framework to explicitly link a count data model with an event-type multinomial-choice model. The proposed framework uses a multinomial probit kernel for the event-type choice model and introduces unobserved heterogeneity in both the count and discrete-choice components. Additionally, this paper establishes important new results regarding the distribution of the maximum of multivariate normally distributed variables, which form the basis to embed the multinomial probit model within a joint modeling system for multivariate count data. The model is applied to analyzing out-of-home non-work episodes pursued by workers, using data from the National Household Travel Survey.