Recently, various infrastructure-assisted or onboard driving assistant applications have been proposed as a component of intelligent transportation systems (ITS) to improve the transportation system’s efficiency and release public concern about road safety. However, such AI-assisted intelligent applications are mainly data-driven and put great demands on the computing power of the ITS systems. Therefore, in the highly dynamic Internet-of-Vehicles environment in ITS, how to effectively coordinate the limited computing power of the various components of the system and realize reliable support for such resource-consuming applications through efficient resource allocation methods is the focus of our research. Accordingly, a novel joint computing and communication resource scheduling method is proposed to fulfill those ITS applications’ inherent heterogeneous quality of service (QoS) requirements. By fully exploiting the computing resources provided by the onboard computing device, the edge computing device located in the vehicle’s proximity and remote data center, we designed a hierarchical three-layer Vehicular Edge Computing (VEC) framework. Briefly, an onboard joint computation offloading and transmission scheduling policy is designed to assign corresponding offloading decisions to the locally generated computing tasks by considering the vehicle’s computing resources and real-time network link status. Additionally, a new distributed resource allocation policy is developed for the edge devices, in which we derive a server selection policy and allocate communication time based on our proposed metric. To evaluate the performance and validate the effectiveness of our proposed method, we conduct extensive simulation tests and ablation experiments, respectively. The results show that our approach can achieve stable performance in various experimental settings. Also, compared to the state-of-the-art algorithms, our joint resource allocation policy significantly reduces the scheduling overhead, improves the utilization of system resources, and minimizes the data transmission delay caused by vehicle motion.