Although BICM can significantly improves the BER performance by iteration processing between the demapping and the decoding in a traditional receiver, its design and performance in PNC system has fewer studied. This paper investigates a bit interleaved coded modulation (BICM) scheme in a Gaussian two-way relay channel operated with physical layer network coding (PNC). In particular, we first present an iterative demapping and decoding framework specially designed for PNC. After that, we compare different constellation mapping schemes in this framework, with the convergence analysis by using the EXIT chart. It is found that the anti-Gray mapping outperforms the Gray mapping, which is the best mapping in the traditional decoding schemes. Finally, the numerical simulation shows the better performance of our framework and verifies the mapping design.