Truck-involved crashes, especially truck-car crashes, are associated with serious and even fatal injuries, thus necessitating an in-depth analysis. Prior research focused solely on examining the injury severity of truck drivers or developed separate performance models for truck and car drivers. However, the severity of injuries to both drivers in the same truck-car crash may be interrelated, and influencing factors of injury severities sustained by the two parties may differ. To address these concerns, a random parameter bivariate probit model with heterogeneity in means (RPBPHM) is applied to examine factors affecting the injury severity of both drivers in the same truck-car crash and how these factors change over the years. Using truck-car crash data from 2017 to 2019 in the UK, the dependent variable is defined as slight injury and serious injury or fatality. Factors such as driver, vehicle, road, and environmental characteristics are statistically analyzed in this study. According to the findings, the RPBPHM model demonstrated a remarkable statistical fit, and a positive correlation was observed between the two drivers' injury severity in truck-car crashes. More importantly, the effects of the explanatory factors showing relatively temporal stability vary across different types of vehicle crashes. For example, car driver improper actions and lane changing by trucks, have a significant interactive effect on the severity of injuries sustained by drivers involved collisions between trucks and cars. Male truck drivers, young truck drivers, older truck drivers, and truck drivers' improper actions, elevate the estimated odds of only truck drivers; while older car and unsignalized crossing increase the possibility of injury severity of only car drivers. Finally, due to shared unobserved crash-specific factors, the 30-mph speed limit, dark no lights, and head-on collision, significantly affect the severity of injuries sustained by drivers involved in collisions between trucks and cars. The modeling approach provides a novel framework for jointly analyzing truck-involved crash injury severities. The findings will help policymakers take the necessary actions to reduce truck-car crashes by implementing appropriate and accurate safety countermeasures.@en