The absorbent article of claim 1, wherein the inner nonwoven filament web comprises a polymer selected from the group consisting of polyethylene, polypropylene, copolymers of mainly ethylene and C3-C12 alpha-olefins (commonly known as linear low density polyethylene), copolymers of mainly propylene with ethylene and/or C4-C12 alpha-olefins, flexible polyolefins including propylene-based polymers h