In this study, a drone routing problem is studied, in which several drones are used to perform an initial surveillance on an area after a disaster. During the surveillance, observations are performed by taking photos of nodes representing populated areas and road segments in the network using cameras installed on the drones from two different altitudes. More target nodes and edges can be observed by the drones from the higher altitude, but with low photo quality, while high photo quality can be obtained from the lower altitude, but within a smaller observation range. Each drone has a limited battery capacity and may need to return to the base for charging. Developed methods for the well-known arc-routing and vehicle routing problems cannot be directly used to solve the considered problem. This study aims to route the drones efficiently to perform the observation and satisfy the required photo quality for all target nodes and edges, while minimizing the total time required to perform the surveillance. This paper is the first study which considers the multiple-drone routing problem with different flying altitudes and battery charging process. The problem is formulated as a mixed integer programming model and numerical experiments are provided. Various important future research topics in this drone surveillance routing problem are also identified, which are necessary for providing basics for the development of algorithms to deploy the drones efficiently.