Full-duplex (FD) radio has been introduced for bidirectional communications on the same temporal and spectral resources so as to maximize spectral efficiency. In this paper, motivated by the recent advances in FD radios, we provide a foundation for hybrid-duplex heterogeneous networks (HDHNs), composed of multi-tier networks with a mixture of access points (APs), operating either in bidirectional FD mode or downlink half-duplex (HD) mode. Specifically, we characterize the net- work interference from FD-mode cells, and derive the HDHN throughput by accounting for AP spatial density, self-interference cancellation (IC) capability, and transmission power of APs and users. By quantifying the HDHN throughput, we present the effect of network parameters and the self-IC capability on the HDHN throughput, and show the superiority of FD mode for larger AP densities (i.e., larger network interference and shorter communication distance) or higher self-IC capability. Furthermore, our results show operating all APs in FD or HD achieves higher throughput compared to the mixture of two mode APs in each tier network, and introducing hybrid-duplex for different tier networks improves the heterogenous network throughput.