In this paper, we consider a decode-and-forward (DF) two-way relay (TWR) system in power line communication (PLC). The DF TWR employs physical- layer network coding (PNC). We derive analytic expressions for the average capacity and the outage probability of the system over a log-normal fading channel. Analytic results are verified through Monte Carlo simulations. From the results, the TWR is able to mitigate the half-duplex (HD) spectral efficiency loss incurred by one-way relaying. The impact of the impulsive noise on the system performance is also highlighted in the simulation results. It is shown that higher impulsive probability degrades system performance.