The rapid development of intelligent transportation systems has intensified the demand for real-time and highly reliable computing services, driving the evolution of vehicular edge computing toward more dynamic and flexible collaborative architectures. Multi-layer aerial networks overcome the inherent limitations of traditional ground infrastructure in terms of coverage and service continuity, emerging as a promising supplement and development trend for vehicular edge computing. To this end, a multi-layer aerial edge computing architecture integrating High Altitude Platform (HAP) and Unmanned Aerial Vehicle (UAV) is proposed, collaboratively providing efficient computing support for moving vehicles in the Internet of Vehicles(IoV). To address frequent aerial cell handovers caused by vehicle mobility, a novel handover-aware mechanism is introduced to predict the time window for cell switching under UAV coverage. Under the energy constraints of both vehicles and UAV, the bandwidth partitioning, computing resource allocation, and task offloading decisions are jointly optimized to minimize total task latency and mitigate handover-induced service interruptions. Moreover, to tackle the high computation complexity of the Mixed Integer Nonlinear Programming (MINLP) problem, a three-step iterative algorithm is designed. This algorithm decomposes the problem into subproblems of bandwidth allocation, computing resource allocation, and offloading decision optimization, which can be solved using the CVX tool, linear relaxation, and Alternating Direction Method of Multipliers (ADMM), respectively. Simulation results demonstrate that compared to baseline schemes, the proposed solution reduces total task latency by 11.9%, 23.3% and 25.5% for task sizes ranging from 5~9 Mb, respectively.