Flexible ballistic resistant composite material that has improved resistance to pick-up of water and other liquids, the composite material comprising a plurality of non-woven fibrous layers. The fibrous layers are formed from a network of high tenacity fibers (aramid fibers, extended chain polyethylene fibers and/or rigid rod fibers). The fibers are embedded in a matrix of a thermoplastic polyurethane resin. Preferably, at least two adjacent fiber layers are oriented in a cross-ply arrangement with respect to each other. Flexible armor, such as body vests, are provided which are formed at least in part from the flexible composite material.