Travel planning involves multiple interdependent decisions. Existing literatures have conducted research on the decision-making behavior of travelers without exploring this interdependence. This study conducted an analysis of exploring traveler's decision-making behavior between mode choice and itinerary, by using paper based survey data of air arrival visitors to the Jeju Island. It is interesting to inquire if itinerary of traveler is dependent on mode chosen or a mode is chosen according to the travel itinerary. To accomplish this, new methodological framework, copula based discrete count joint model is used. In the joint framework, mode choice is modeled using binary logit model and itinerary is modeled using zero truncated poisson regression model. To represent the interaction between decisions, seven different copula structures are used for each decision order. The results of the analysis show that travelers choose transportation mode first before making an itinerary. In addition, it was confirmed that the unknown common variables between travel itinerary selection and transportation choice have a positive correlation, with student t-copula as their dependency structure. In terms of effect of variables on both decisions, the travel characteristic variables used in the analysis showed statistically high significance except for the day of the week variable. In contrast, socio-demographic variables showed no statistical significance. Our research highlights that, it is necessary to establish a transportation policy that takes into account the specific hierarchical relationship between traveler's itinerary decision and mode selection.