In recent years, the proliferation of Connected Autonomous Vehicles(CAV) has revolutionizing the transportation industry. However, these vehicles often face limitations in terms of local computing resources, leading to the need for offloading interactive-intensive application tasks to servers for processing. Traditional paradigm has its limitations in meeting the demands of massive task processing. The combination of Web3.0 and edge computing offers users high-reliable, low-latency, and highly flexible services. Nevertheless, the new paradigm also presents its own challenges such as ensuring privacy data protection, and reducing the time and energy costs associated with task offloading. To tackle these challenges, a edge task offloading framework based on consortium blockchain for CAVs has been developed. Within this framework, a consortium blockchain-based interaction-intensive task offloading method, called CBIToMe, has been designed. CBIToMe specifically addresses the multi-stage nature of interactive-intensive CAV tasks and aims to minimize task completion time and offloading costs, particularly when the waiting time for interaction is uncertain. Additionally, CBIToMe effectively utilizes consortium blockchain technology to safeguard the CAV privacy data. Results from experiments conducted in various scenarios demonstrate that CBIToMe outperforms three representative methods, showcasing its superior performance.