D2D communication is an effective approach for traffic offloading in future cellular systems. However, only using direct D2D communication is not enough to fully exploit the advantages of D2D communications due to long distances or poor link quality between source and destination D2D UEs. This work aims to enhance the traffic offloading capacity of cellular-assisted D2D communication, taking into account D2D relays. In particular, we propose a unified model for D2D communication, in which two other D2D communication modes, that is, relay-assisted D2D and local route based D2D, are also supported by UEs in addition to direct D2D mode. We design radio protocol architectures for the three D2D modes and propose an eNB scheduling algorithm, which enables the eNB to perform joint scheduling on mode selection, radio resource allocation, and power coordination for all D2D pairs in each subframe. The effectiveness of our designs is validated by simulations.