New materials are needed to replace degenerated intervertebral disc tissue and to provide longer-term solutions for chronic back-pain. Replacement tissue potentially could be engineered by seeding cells into a scaffold that mimics the architecture of natural tissue. Many natural tissues, including the nucleus pulposus (the central region of the intervertebral disc) consist of collagen nanofibers embedded in a gel-like matrix. Recently it was shown that electrospun micro- or nano-fiber structures of considerable thickness can be produced by collecting fibers in an ethanol bath. Here, randomly aligned polycaprolactone electrospun fiber structures up to 50 mm thick are backfilled with alginate hydrogels to form novel composite materials that mimic the fiber-reinforced structure of the nucleus pulposus. The composites are characterized using both indentation and tensile testing. The composites are mechanically robust, exhibiting substantial strain-to-failure. The method presented here provides a way to create large biomimetic scaffolds that more closely mimic the composite structure of natural tissue.