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We consider network coding for the time-division two-way relay channel (TWRC). Based on achievable rates, we study the optimal transmission time allocation for a three-phase transmission protocol. While existing network coding schemes for the TWRC perform "hard" network coding, we propose a novel soft-information-based joint network-channel coding scheme. A detailed description of the operation of each network node in our scheme is given. Moreover, we discuss optimal log-likelihood ratio quantization as well as the transmission of quantized soft information. Finally, we assess the performance of the proposed scheme using numerical simulations, including a comparison to conventional "hard" network coding and to direct transmission without relay.