Heterogeneous device services generated by various devices in different contexts prevent users from efficiently and correctly consuming device services. This seriously hinders the development of Internet of Things. This paper addresses the problems appearing in device discovery and device interaction. It devises a user interoperability framework (UIF) to enable device users to interoperate with heterogeneous devices of different contexts with consistent syntax and semantics. In this framework, a new separation strategy is provided; a device representation method for real, common, and virtual devices is devised; and a device transformability model is proposed to guarantee the proper transformation of device syntax and semantics. To demonstrate the correctness of UIF, a UIF prototype is implemented and several experiment methods are compared to determine which one should be adopted as semantic relatedness computing tools in device discovery for device users and in common device publishing for device providers.