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Activity start time and duration decisions are two key elements of activity-travel behavior. As an effort toward a more realistic representation of individuals' decision behavior, this paper presents a new copula-based joint model of activity start time and duration decisions. The authors incorporate the regret theory into the joint modeling framework, which assumes that individuals tend to avoid the situation where non-chosen alternatives outperform the chosen one in one or more attributes. The proposed joint model comprises a hybrid utility-regret model as the discrete component to estimate activity start time and a hazard duration model as the continuous component to estimate activity duration. The comparative analysis of estimation results reveals that the proposed structure is statistically superior to the utility-based joint model and independent models. The authors also found that applying the regret-based decision rule for variables of travel time, travel time variability, and individuals’ schedule occupancy significantly improves the model. Furthermore, the significance of the estimated copula parameters confirms the existence of unobserved shared factors between the two considered activity attributes, which entails the use of joint modeling scheme.