One-dimensional nanomaterials such as carbon nanotubes (CNTs) and boron nitride nanotubes (BNNTs) possess impressive physical, chemical and mechanical properties and are promising reinforcement agents for the development of enhanced composites with added functionalities. Here we show the fabrication of CNT-polyurethane (TPU) and BNNT-TPU sheets of variable composition using a scalable one-step filtration process. Using this fabrication method the composition of the nanocomposites, which defines the characteristics and properties of the material, can be precisely controlled. Consequently, materials with tailorable properties (e.g. porosity, stiffness, strength and toughness and adhesion) and functionalities can be fabricated. At specific NT-TPU weight ratios (e.g., 35:65 for CNT-TPU composites) a better NT exfoliation and optimal NT surface coverage was achieved, which led to an optimal packing of NT−TPU fibers. This optimal packing produced the highest improvement in tensile properties and electrical conductivity in CNT-TPU sheets. Due to their straightforward production and handling, high nanotube content, and superior properties in comparison to dispersed NT composites, the resulting conductive, lightweight sheets are of interest for various applications including improved damage tolerance and electrical properties of laminate composites, self-sensing and electromagnetic shielding. On the other hand, thermally conductive (4 W/m·K), electrically insulating sheets were produced with BNNTs. Nano-microscale roughness, which is essential for superhydrophobicity, can also be integrated on the CNT-TPU and BNNT-TPU fabric surface during the fabrication method by a novel approach that incorporates a nano-micron size array of functionalized nanotubes (CNTs or BNNTs) on the sheet surface producing highly non-wetting surfaces. Sheets can also be applied as coatings on other structures (e.g. glass fiber reinforced plastics) to create a multifunctional self-cleaning surfaces.