One or more nanofiber yarns can be placed in contact with one or more nanofiber sheets. The nanofiber yarns, which include single-ply and multi-ply nanofiber yarns, provide added mechanical stability to a nanofiber sheet that decreases the likelihood of a nanofiber sheet wrinkling, folding, or otherwise becoming stuck to itself. Furthermore, the nanofiber yarns integrated with the nanofiber sheet can also act as a mechanism to prevent the propagation of tears through the nanofiber sheet. In some cases, an infiltrating material can be infiltrated into interstitial spaces defined by the nanofibers within both the nanofiber yarns and the nanofiber sheets. The infiltrating material can then form a continuous network throughout the nanofiber yarns and the nanofiber sheet.