This paper investigates information freshness of two-way relay networks (TWRNs) operated with physical-layer network coding (PNC). Information freshness is quantified by age of information (AoI), defined as the time elapsed since the generation time of the latest received information update. PNC reduces communication latency of TWRNs by turning superimposed electromagnetic waves into network-coded messages so that end users can send update packets to each other more frequently via the relay. While sending update packets more frequently has the potential to reduce AoI, how to handle packet corruption has not been investigated. Specifically, if an old packet is corrupted in any hop of a TWRN, one needs to decide whether to drop or to retransmit the old packet. Therefore, we study the average AoI with and without automatic repeat request (ARQ) in PNC-enabled TWRNs. Interestingly, our analysis shows that neither the non-ARQ scheme nor the pure ARQ scheme achieves a good average AoI. Hence, we put forth an uplink-lost-then-drop (ULTD) protocol that combines packet drop and ARQ. Experiments on software-defined radios indicate that ULTD significantly outperforms non-ARQ and pure ARQ schemes in terms of average AoI, especially when the two end users have imbalanced channel conditions. We believe the insight of ULTD on TWRNs generally applies to other two-hop networks. Copyright © 2022 IEEE.