Aerial base stations are a promising technology to increase the capabilities of existing communication networks. However, existing analytical frameworks do not sufficiently characterize the impact of ground interferers on aerial base stations. In order to address this issue, we model the effect of interference coming from coexisting ground networks on the aerial link, which could be the uplink of an aerial cell served by a drone base station. By considering a Poisson field of ground interferers, we characterize aggregate interference experienced by the drone. This result includes the effect of drone antenna pattern, the height-dependent shadowing, and various types of environment. We show that benefits a drone obtains from a better line-of-sight (LoS) at high altitudes is counteracted by a high vulnerability to the interference coming from ground. However, by deriving link coverage probability and transmission rate we show that a drone base station is still a promising technology if the overall system is properly dimensioned according to given density and transmission power of interferers. Particularly, our results illustrate how benefits of such network is maximized by defining the optimal drone altitude and signal-to-interference (SIR) requirement.