White-light observations of coronal mass ejections (CMEs) often show the classic three-part structure consisting of (1) a bright front; (2) a dark cavity; and (3) a bright, compact core. It has proven difficult to unambiguously associate these features with in situ measurements of interplanetary CMEs (ICMEs), in all but a few cases. In this study we use a global MHD model to simulate the eruption and evolution of a CME out to 0.25 AU, allowing us to continuously track these features from the Sun and through the solar wind. Our results support the generally held view that the interplanetary flux rope corresponds to the dark cavity. We find that the bright front merges with solar wind material swept up by the ICME. Thus, the sheath material found ahead of fast ejecta is in fact composed from both ambient solar wind material, as well the bright front. We also note that, in this simulation, the bright front is formed from the overlying streamer configuration from within which the CME erupted and is not itself coronal material swept up during the early phase of the eruption. The conclusions reached in this study are undoubtedly sensitive to the initial configuration and mechanism used to initiate the CME, and thus care should be taken when using them to interpret specific observations. On the other hand, they provide a unique, unbroken connection between remote solar and interplanetary observations. Ultimately, detailed comparisons between observations and simulation results may be able to constrain or even rule out some mechanisms of CME initiation.