Due to the asynchronous development of observation and transition capabilities, the original image data (OID) obtained by a one-time observation cannot be completely transmitted in one transmission cycle between the EOS and GS, which is named a visible time window (VTW). First, it is needed to segment the OID into several segmented image datasets (SIDs), which are then transmitted in several VTWs. Furthermore, this can cause the satellite image data downlink scheduling problem (SIDSP). This study defines an innovative SIDSP as a satellite image data downlink scheduling problem with the family attribute (SIDSPFA), where massive OID are segmented using a fast segmentation operator, and all SIDs and other no-segmented OID are transmitted in the second step. In addition, two optimization objectives, namely the failure rate (FR) and Segmentation Time (ST) of the image data transmission, are defined to formalize the SIDSPFA as a bi-objective discrete optimization model. Further, a bi-stage differential evolutionary algorithm (DE-CD) is developed. The results of the extensive simulation tests verify the efficiency of the models, strategies, algorithms, and operators used in this study.