Radio-frequency energy harvesting constitutes an effective way to prolong the lifetime of wireless networks, wean communication devices off the battery and power line, benefit the energy saving and lower the carbon footprint of wireless communications. In this paper, an interference aided energy harvesting scheme is proposed for cooperative relaying systems, where energy-constrained relays harvest energy from the received information signal and co-channel interference signals, and then use that harvested energy to forward the correctly decoded signal to the destination. The time-switching scheme (TS), in which the receiver switches between decoding information and harvesting energy, as well as the power-splitting scheme (PS), where a portion of the received power is used for energy harvesting and the remaining power is utilized for information processing, are adopted separately. Applying the proposed energy harvesting approach to a decode-and-forward relaying system with the three-terminal model, the analytical expressions of the ergodic capacity and the outage capacity are derived, and the corresponding achievable throughputs are determined. Comparative results are provided and show that PS is superior to TS at high signal-to-noise ratio (SNR) in terms of throughput, while at low SNR, TS outperforms PS. Furthermore, considering different interference power distributions with equal aggregate interference power at the relay, the corresponding system capacity relationship, i.e., the ordering of capacities, is obtained.