Two-path successive relaying (TPSR) is an effective way to reduce the multiplex loss induced by the half-duplex operation of the relay node in a conventional relay network. One crucial issue in TPSR network is that the listening relay always suffers inevitable inter-relay interference (IRI), which degrades detection performance at the destination. In this study, a concatenated channel-and-network coding approach is proposed to solve the problem. In particular, a highly flexible channel code, namely, rateless code, is employed at the source to provide resilience to the residual IRI and reduce the retransmissions, which might break the system steady state of successive relaying. Then recognising the special interference structure, physical-layer network coding is incorporated into the forwarding scheme of the relay nodes to exploit network diversity and improve system efficiency. By extrinsic information transfer analysis, the minimum number of required code symbols for successful data recovery are calculated, and degree distribution of the rateless code is optimised.