Steel sheet-viscoelastic core laminates are often subject to corrosion in moisture-containing environments. Zinc-based alloys of iron may be beneficially applied to the inner faces of the steel sheets or to both the inner and outer sheet faces. Substantially pure zinc coatings may be applied over the zinc-iron alloys or over an otherwise base outer steel sheet surface. Combinations of such zinc-iron alloy coatings and substantially pure zinc coatings improve the corrosion resistance of the steel sheet-polymer core laminates while supporting weldability and paintability.