Coronal mass ejections (CMEs) can be continuously tracked through a large portion of the inner heliosphere by direct imaging in visible and radio wavebands. White-light (WL) signatures of solar wind transients, such as CMEs, result from Thomson scattering of sunlight by free electrons, and therefore depend on both the viewing geometry and the electron density. The Faraday rotation (FR) of radio waves from extragalactic pulsars and quasars, which arises due to the presence of such solar wind features, depends on the line-of-sight magnetic field component $B_∥$, and the electron density. To understand coordinated WL and FR observations of CMEs, we perform forward magnetohydrodynamic modelling of an Earth-directed shock and synthesise the signatures that would be remotely sensed at a number of widely distributed vantage points in the inner heliosphere. Removal of the background solar wind contribution reveals the shock-associated enhancements in WL and FR. While the efficiency of Thomson scattering depends on scattering angle, WL radiance $I$ decreases with heliocentric distance $r$ roughly according to the expression $I ∝ r^{-3}$. The sheath region downstream of the Earth-directed shock is well viewed from the L4 and L5 Lagrangian points, demonstrating the benefits of these points in terms of space weather forecasting. The spatial position of the main scattering site $𝐫_{\rm sheath}$ and the mass of plasma at that position $M_{\rm sheath}$ can be inferred from the polarisation of the shock-associated enhancement in WL radiance. From the FR measurements, the local $B_{∥ {\rm sheath}}$ at $𝐫_{\rm sheath}$ can then be estimated. Simultaneous observations in polarised WL and FR can not only be used to detect CMEs, but also to diagnose their plasma and magnetic field properties. ; Comment: 20 pages, 11 figures, 1 table. To be published by Astrophys. J., 2013