Space weather research requires investigation of a complex chain of coupled dynamic phenomena occurring simultaneously on various spatial and temporal scales between the Sun and Earth. Specialized physically based numerical models have been developed to address particular aspects of the entire system. However, an integrated modeling approach is necessary to provide a complete picture suitable for interpretation of various remote and in situ observations and for development of forecasting capabilities. In this paper we demonstrate merging of coronal and heliospheric MHD models for a two-dimensional hypothetical case involving a magnetic cloud, shock, streamer belt, and current sheet. The disruption of a sheared helmet streamer launches a coronal mass ejection (CME) (simulated by the coronal model), which evolves during its propagation through interplanetary space (simulated by the heliospheric model). These models employ different physical approximations and numerical grids to simulate physical phenomena over their respective spatial and temporal domains. The merging of the models enables accurate tracking of a CME from its origin in the solar atmosphere to its arrival at Earth.