A physical interpretation of observed coronal on-disk manifestations of an Earth-directed coronal mass ejection (CME) is presented. The fundamental question of how the CME's magnetic field and its plasma distribution are related is largely unanswered, because a crucial piece of the puzzle, that is the three-dimensional (3-D) morphology of the CME, remains difficult to ascertain so long as coronal observations are limited to projections onto a single plane of the sky. In order to understand the relationship between observations of CMEs projected at the solar limb and those projected on the solar disk, some sort of model of the 3-D CME is required. In this paper we address both the question of the 3-D morphology of the CME and the more fundamental question of the nature of the plasma-magnetic field relationship, by comparing the limb and on-disk CME representations of an analytic 3-D MHD model based on a spheromak-type flux rope magnetic field configuration. In particular, we show that the morphology of twin dimmings (also referred to as transient coronal holes) observed in X ray and EUV can be reproduced by the CME model as the on-disk projection of the prominence cavity modeled for limb CMEs. Moreover, the bright core of a limb CME, generally corresponding to the material in an erupting prominence, may be interpreted to be the S-shaped central core of the modeled on-disk CME, splitting the cavity into twin dimmings when observed head-on without obstruction. The magnetic field structure of this central core exhibits many of a filament's magnetic field features required to match observations. Finally, we consider the nature of S-shaped filaments and X-ray sigmoids in the context of the model, in terms of localized heating and cooling acting on the modeled CME magnetic field structure. ¿ 2000 American Geophysical Union