In this paper, an Air-Ground Integrated VEhicular Network (AGIVEN) architecture is proposed, where the aerial High Altitude Platforms (HAPs) proactively push contents to vehicles through large-area broadcast while the ground roadside units (RSUs) provide high-rate unicast services on demand. To efficiently manage the multi-dimensional heterogeneous resources, a service-oriented network slicing approach is introduced, where the AGIVEN is virtually divided into multiple slices and each slice supports a specific application with guaranteed quality of service (QoS). Specifically, the fundamental problem of multi-resource provisioning in AGIVEN slicing is investigated, by taking into account typical vehicular applications of location-based map and popularity-based content services. For the location-based map service, the capability of HAP-vehicle proactive pushing is derived with respect to the HAP broadcast rate and vehicle cache size, wherein a saddle point exists indicating the optimal communication-cache resource trading. For the popular contents of common interests, the average on-board content hit ratio is obtained, with HAPs pushing newly generated contents to keep on-board cache fresh. Then, the minimal RSU transmission rate is derived to meet the average delay requirements of each slice. The obtained analytical results reveal the service-dependent resource provisioning and trading relationships among RSU transmission rate, HAP broadcast rate, and vehicle cache size, which provides guidelines for multi-resource network slicing in practice. Simulation results demonstrate that the proposed AGIVEN network slicing approach matches the multi-resources across slices, whereby the RSU transmission rate can be saved by 40% while maintaining the same QoS.