This work focuses on the study of a heterogeneous wireless-powered communication (H-WPCN) system, where a device-to-device (D2D) communication pair is overlaid with a downlink (DL) communication pair. In DL communications, the access point keeps spreading radio frequency (RF) signals to serve the DL user equipment (UE). In addition to being the data source of the UE, DL RF signals are also utilized by the D2D transmitter as the only energy source supporting D2D communications. To capture the impact of limited spectrum resource on the proposed H-WPCN system, co-channel interference is considered. Assuming the Rayleigh block fading channel for signal propagation, a tight lower bound as well as its closed-form approximation are provided for the outage probability of the DL communication link, and an exact expression is derived for the outage probability of the D2D communication link. After that, the throughput of the H-WPCN system is optimized via joint power control and time allocation, where the throughput of the D2D communication link is maximized subject to a required throughput for DL communications. Finally, our theoretical analysis is verified by numerical simulations. The simulation results show that the throughput of the H-WPCN system may not benefit from a high energy conversion efficiency.