Nanofiber sheet assemblies include at least one nanofiber sheet and at least one nanofiber grid or web that is used to improve the physical durability of the nanofiber sheet within the assembly. Nanofiber sheet assemblies retain the permeability of the nanofiber sheets to gaseous phase substances. This enables technological applications of nanofiber sheet assemblies to include filters for micron or nano-scale particles that are disposed in gas phase substances.