The study of relays with the scope of energy-harvesting (EH) looks interesting as a means of enabling sustainable, wireless communication without the need to recharge or replace the battery driving the relays. However, reliability of such communication systems becomes an important design challenge when such relays scavenge energy from the information bearing RF signals received from the source, using the technique of simultaneous wireless information and power transfer (SWIPT). To this aim, this work studies bidirectional communication in a decode-and-forward (DF) relay assisted cooperative wireless network in presence of co-channel interference (CCI). In order to quantify the reliability of the bidirectional communication systems, a closed form expression for the outage probability of the system is derived for both power splitting (PS) and time switching (TS) mode of operation of the relay. Simulation results are used to validate the accuracy of our analytical results and illustrate the dependence of the outage probability on various system parameters, like PS factor, TS factor, and distance of the relay from both the users. Results of performance comparison between PS relaying (PSR) and TS relaying (TSR) schemes are also presented. Besides, simulation results are also used to illustrate the spectral-efficiency and the energy-efficiency of the proposed system. The results show that, both in terms of spectralefficiency and the energy-efficiency, the two-way communication system in presence of moderate CCI power, performs better than the similar system without CCI. Additionally, it is also found that PSR is superior to TSR protocol in terms of peak energy-efficiency.