In this paper, we study joint network/channel decoding for multi-source multi-relay heterogeneous wireless networks. When convolutional and network codes are used at the physical and network layers, respectively, we show that error correction and diversity properties of the whole network can be characterized by an equivalent and distributed convolutional network/channel code. In particular, it is shown that, by properly choosing the network code, the equivalent code can show Unequal Error Protection (UEP) properties, which might be useful for heterogeneous wireless networks in which each source might ask for a different quality-ofservice requirement or error probability. Using this representation, we show that Maximum-Likelihood (ML) joint network/channel decoding can be performed by using the trellis representation of the distributed convolutional network/channel code. Furthermore, to deal with decoding errors at the relays, a ML-optimum receiver which exploits side information on the source-to-relay links is proposed.