As a vital component of disaster response and relief, a wireless network needs to be rapidly deployed after a disaster strikes. Due to the advantages of large area coverage, low capital cost, and fast deployment, an unmanned aerial vehicle (UAV) is believed to be a potentially promising choice to recover wireless communication in post-disaster environments. In this paper, the performance gains of utilizing two cooperative UAVs for downlink transmission over a large number of emergency response rescue vehicles on the ground in post-disaster areas are explored. Toward this end, the concept of average channel access delay for a generic vehicle to establish a full transmission to an UAV is introduced, i.e., data packets are said to be successfully transmitted from a UAV to a vehicle only if the time duration for the vehicle covered by the UAV is greater than the specified average channel access delay. Based on the proposed concept, a stochastic geometry based mathematical framework to analyze the coverage probability and average achievable rate for a multi-UAV-assisted downlink network, where vehicles connect to the Internet via satellites in a two-hop manner, is presented. According to the derived closed-form solutions for the network performance metrics, extensive numerical results are provided to illustrate the network performance gains brought by UAVs. Additionally, optimal settings are also presented for network designers to efficiently determine the optimal network parameters so as to achieve the optimum network performances in post-disaster areas.