Unmanned Aerial Vehicles (UAVs) are being increasingly integrated into humanitarian operations given the growing economic pressure on organisations providing disaster relief. Among other applications, UAV-based damage assessment during relief delivery has been the focus of respondents, yet 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 deployments and relief vehicle dispatches to minimise overall mission cost. The algorithm considers uncertain damage levels in a transport network, with UAVs revealing actual damage levels by performing rapid network assessment. Ground vehicles are simultaneously routed based on the information gathered by the UAVs. A greedy extact solution approach and an adapted Genetic Algorithm are used to solve a case study based on the 2010 Haiti earthquake. Both approaches provide significant improvements in vehicle travel time over a deterministic approach reported, and are used to quantify the benefits of UAV-assisted response.