Reliable transmission of a discrete memoryless source over a multiple-relay network is considered. Motivated by sensor network applications, it is assumed that the relays and the destination all have access to side information correlated with the underlying source signal. Joint source-channel cooperative transmission is studied in which the relays help the transmission of the source signal to the destination by using both their overheard signals, as in the classical channel cooperation scenario, and the available correlated side information. Decode-and-forward (DF) based cooperative transmission is considered in a network of multiple relay terminals and two different achievability schemes are proposed: i) a regular encoding and sliding-window decoding scheme with no binning at the encoder, and ii) a semi-regular encoding and backward decoding scheme with explicit binning based on the side information statistics. It is shown that both of these schemes lead to the same sufficiency conditions, which are shown to be also necessary in the case of a physically degraded relay network in which the side information signals are also degraded in the same order.