Electronic Health (eHealth), especially in the form of electronic health records (eHRs), has proved to be helpful in health care services both in urban and remote areas. However, many of the systems are fragmented and work independently. Therefore, apart from their benefits, these systems are stand alone and as such they face some operational challenges. One of which is interoperability among the eHRs. Early efforts to interoperate eHealth systems, suggest that a single mobile application that can access multiple integrated eHRs is among the viable solutions on the way to eHRs interoperability. The proposed data exchange approach offers a mechanism to integrate a single mobile application with multiple eHRs while mitigating the interoperability problem. The design work builds on the results of a survey previously done to collect preliminary requirements of the data exchange system. System design techniques were used to design this system. In this paper, an architectural system design of an eHealth data exchange that can mitigate the interoperability challenge is presented.