Presented are multilayer, fiber-reinforced impact protection structures with honeycomb-core or corrugated-layer designs, methods for making/using such structures, and vehicles with traction battery packs supported on skid plates fabricated from such structures. A multilayer impact protection structure includes a first layer with continuous fibers embedded in a polymeric matrix, and a second layer that is attached to the first layer and includes an elastomeric polymer. A third layer, which is attached to one side of the first layer opposite that of the second layer, includes a fiber-reinforced polymer honeycomb and/or corrugated structure. An optional fracture detection circuit is attached to the first or third layer, and is configured to detect a break in the impact protection structure. The corrugated structure may include multiple reinforcement ribs that are interposed within and substantially orthogonal to a series of mutually parallel, elongated ridges. Comparatively, the honeycomb structure includes a lattice of adjoining polygonal cells.