In a densely distributed sensor network, it is known that it is advantageous to exploit both intra- and inter- signal correlation structures during recovery procedure. Based on this observation, the bound of the required number of measurement in distributed compressive sensing (DCS) is shown to be reduced by exploiting this structure. In this paper, we generalize the model for distributed compressive sensing and show that elaborated signal structure can reduce the required number of measurements further. To this end, we introduce a new concept of partial common information which is shared by some parts of signals, but not by every signal. Numerical results show that with the proposed model, more robust signal recovery can be achieved.