Escalating motorcycle crashes present a significant challenge due to the increase in motorcycle registrations and the corresponding increase in mortality rates. This issue is particularly acute in Cambodia, where motorcycles are the primary mode of transportation. In the analysis of motorcycle crashes, two key measures of severity are injury severity and crash size, notably the number of injuries. Typically, these indicators are analyzed independently to understand the impact and consequences of motorcycle accidents. Nevertheless, it is critical to recognize that both observed and unobserved factors may concurrently affect these crash indicators, indicating a possible interrelationship between injury severity and motorcycle crash size. Neglecting the joint occurrence of these variables can result in biased and incorrect parameter estimation. This research contributes to the existing body of knowledge by simultaneously analyzing the factors influencing both injury severity and motorcycle crash size. This approach further distinguishes itself by considering the interdependence between these two results utilizing a copula-based approach. Six models based on copulas were developed using the ordered logit model, which was designed to capture the ordinal nature of injury severity and crash size. By analyzing motorcycle crash data from 2016 in Cambodia, the Frank copula framework was identified as the most effective among the five approaches. The findings revealed that factors such as motorcycle-to-pedestrian collisions, head-on collisions, X junctions, and national roads significantly increase both motorcyclist injury severity and crash size. These insights are valuable for policymakers in formulating targeted strategies to improve motorcycle safety within transportation systems.