Unmanned aerial vehicles (UAVs) have been increasingly viewed as useful tools to assist humanitarian response in recent years. While organisations already employ UAVs for damage assessment during relief delivery, there is a lack of research into formalising a problem that considers both aspects simultaneously. This paper presents a novel endogenous stochastic vehicle routing problem that coordinates UAV and relief vehicle deployments to minimise overall mission cost. The algorithm considers stochastic damage levels in a transport network, with UAVs surveying the network to determine the actual network damages. Ground vehicles are simultaneously routed based on the information gathered by the UAVs. A case study based on the Haiti road network is solved using a greedy solution approach and an adapted genetic algorithm. Both methods provide a significant improvement in vehicle travel time compared to a deterministic approach and a non-assisted relief delivery operation, demonstrating the benefits of UAV-assisted response.