This paper studies the performance of a half-duplex (HD) two-way relay (TWR) in power line communication (PLC) over a log-normal fading channel with impulsive noise. We consider the two common relaying protocols: amplify-and-forward (AF) and decode-and-forward (DF). For the DF relaying, we apply physical-layer network coding (PNC) and analog-network coding (ANC) to the PLC TWR. We derive analytic expressions for the average sum capacity and the outage probability of the system. The Monte Carlo simulations are provided throughout to validate our analysis. The analytical results show a tight approximation to the simulation results. We compare the one-way relay (OWR) to the TWR and show that the HD spectral efficiency loss incurred by the OWR can be sufficiently mitigated in PLC. However, the outage probability of the TWR is inferior to that of the OWR. To enhance the outage performance of the PLC TWR, we implement a hybrid PLC/wireless (HPW) system, where all nodes are equipped with the PLC and wireless capabilities. Data transmission occurs over the two parallel links. The diversity in the transmission allows the TWR to improve its outage performance in the AF and DF protocols. The impact of the impulsive noise, inherent to the PLC channels, is also highlighted in the simulation results. It is shown that the impulsive noise severely impairs system performance. INDEX TERMS Two-way relaying, average capacity, outage probability, power line communication (PLC), PLC/wireless diversity.