SUMMARY Controlled-source electromagnetic prospecting systems which produce vertical current flow in the Earth are sensitive to horizontal, electrically resistive structures such as hydrocarbon deposits and fresh water lenses. The electromagnetic response of such 3-D targets can sometimes be approximated by the fields produced by an arrangement of thin resistive sheets buried in a conductive host medium. We have previously shown, through simplified 2-D modelling, that the resistive sheet problem is more subtle than the conductive case commonly used in mineral exploration. Not only does the resistive sheet require the continuity of the normal current density as opposed to the continuity of the tangential electric field, interaction terms within the coupling matrix must also be calculated in full rather than approximated by point dipole sources representing each element. The purpose of this paper is to extend these results to the more realistic and practical situation of a 3-D resistive sheet buried in a multilayered earth. The algorithm is validated against 1-D calculations for a very large sheet and 3-D finite difference modelling for a smaller sheet. A current deflection number characterizes the effect of a resistive sheet's transverse impedance and governs its response in the same way that the current channelling number does for a conductive target. The sheet can be represented to first order by a single point dipole located at its centre; at most receiver locations, arrival times are nearly identical to those found from the full solution although amplitudes show some deviation near the target. As an example of the use of the algorithm, the marine controlled-source electromagnetic response of a simple anticlinal hydrocarbon reservoir underlying near surface resistors such as shallow gas or gas hydrate deposits is modelled. Results show that such near surface anomalies, even those with low deflection numbers, significantly affect the response of the deeper target and must be included in modelling and interpretation.