In this study, the authors first analyse system performance of beamforming amplify-and-forward two-way relay networks with physical-layer network coding under the impact of co-channel interference from multiple surrounding terminals and then propose the associated power allocation strategies. The performance of the two-way communications in terms of outage probability, symbol error rate (SER), and total ergodic channel capacity of the system is quantified. Asymptotic performance analysis for sufficiently high signal-to-noise ratio is also provided to obtain further valuable insights into system designs. Based on the analysis, power allocation strategies to minimise the asymptotic outage probability and SER as well as to maximise the ergodic channel capacity under the total power constraint are developed. The numerical results show that the proposed power allocation approaches outperform equal power allocation given the same total power budget and other system parameters. © The Institution of Engineering and Technology.