Self-sustainable communications based on advanced energy harvesting technologies have been under rapid development, which facilitate autonomous operation and energy-efficient transmission. Recently, ambient backscattering that leverages existing RF signal resources in the air has been invented to empower data communication among low-power devices. In this paper, we introduce hybrid device-to-device (D2D) communications by integrating ambient backscattering and wireless-powered communications. The hybrid D2D communications are self-sustainable, as no dedicated external power supply is required. However, since the radio signals for energy harvesting and backscattering come from external RF sources, the performance of the hybrid D2D communications needs to be optimized efficiently. As such, we design two mode selection protocols for the hybrid D2D transmitter, allowing a more flexible adaptation to the environment. We then introduce analytical models to characterize the impacts of the considered environment factors, e.g., distribution, spatial density, and transmission load of the ambient transmitters, on the hybrid D2D communications performance. Extensive simulations show that the repulsion factor among the ambient transmitters has a non-trivial impact on the communication performance. Additionally, we reveal how different mode selection protocols affect the performance metrics.