As policymakers suggest using Transportation Demand Management (TDM) strategies, understanding the roots of the differences between the predicted and actual results of these policies' implementation is an area of interest for research. Among diverse reasons studies identify for this gap, this study focuses on model capabilities, using copula-based joint models for modal shift and mode choice. The study offered a hypothetical bundle of TDM strategies to 577 commuters who regularly drove to their workplaces during peak hours. Their stated mode choices were gathered. Thereupon, two successive steps were captured from their decision-making process: first, the decision to give up driving or not, and second, the substitute chosen mode if leaving driving was adopted. The joint effect of changing/not changing the travel mode from a private car and picking an alternative while facing a package of TDM strategies was tested with the copula approach. A binary logit is used to model the mode change decision, and the mode choice is modelled using a multinomial logit. Finally, among several copula functions, Frank Copula with the highest maximum likelihood estimation, and the positive value of dependency parameter, with an adjusted ρ2 of 0.158 was chosen as the best model. The findings of this study highlight the importance of considering people's previous mode decisions while trying to increase transit and decrease private use with TDM policies, which was not addressed in the literature using a dependent joint structure.