We consider the code design for a half-duplex 4-node joint relay system with two sources, one relay, and one destination. The relay combines the information from both sources and transmits it to the destination together with both sources. We consider two coding schemes for information combining at the relay, namely, the superposition coding (SC) and the Raptor coding (RC). The Raptor codes are employed at the sources as well as the relay. The relay and the destination perform iterative a posteriori probability (APP) detection and soft Raptor decoding. For both SC and RC, the profiles for Raptor codes are optimized based on the extrinsic information transfer (EXIT) function analysis. For both the additive white Gaussian noise (AWGN) and block fading channels, the joint relay system with optimized profiles exhibits significant performance gains over that employing the code profile optimized for either the singleuser AWGN channel or the 2-user multiple-access channel.