Recent years have witnessed a surge in the deployment of Deep Neural Network (DNN)-based services, which drives the development of emerging intelligent transportation systems (ITSs). However, it is still challenging to enable efficient and reliable DNN inference in Vehicular Edge Computing (VEC) environments due to resource constraints and system dynamics. In view of this, this work investigates a DNN inference partition and offloading scenario with environmental uncertainties in VEC, which motivates the necessity to strike a balance between inference delay and the success ratio of receiving the offloading outputs. Then, by considering communication and computation overheads as well as failed offloading conditions in an analytical model, we propose an Adaptive Splitting, Partitioning, and Merging (ASPM) strategy that reduces the inference delay while maintaining a decent offloading success ratio. Specifically, ASPM first splits and partitions the DNN model in a recursive way to find the optimal split blocks with the aim of minimizing inference delay. On this basis, it further merges DNN blocks in a greedy way to reduce the number of blocks to be offloaded thus, enhancing the offloading success ratio for the whole DNN inference. Finally, we conduct comprehensive performance evaluations to demonstrate the superiority of our design.