Drone small cells (DSCs) are served as aerial base stations to complement the terrestrial cellular networks, in order to provide seamless wireless coverage and increased network capacity. In this paper, we study a drone-assisted downlink heterogeneous network (HetNet) consisting of a first tier of DSCs overlaid with a second tier of terrestrial small cells (TSCs), both of which operate on the same frequency band. By considering a flexible biased association policy, we develop an analytical framework to evaluate the network performance. After deriving the association probabilities, and the probability distribution functions (PDFs) of typical link length, we derive exact expressions for the per-tier and overall coverage probabilities. The proposed framework allows to quantify the impact on network performance of most important system parameters, such as the height of DSCs, the bias factor, and the base station density. In absence of interference management, our results show that very limited gains can be obtained in the dense network scenario and the improper deployment of DSCs can only degrade the coverage probability achieved by the single-tier TSC network. What's more, the unbiased cell association is shown to be optimal for the overall coverage probability in the interference-limited network regime.