A building structure containing a building envelope that defines an interior is provided. The building structure includes building insulation positioned adjacent to a surface of the building envelope, the interior, or a combination thereof. The building insulation may include a porous polymeric material that is formed from a thermoplastic composition containing a continuous phase that includes a matrix polymer. A microinclusion additive and nanoinclusion additive may also be dispersed within the continuous phase in the form of discrete domains, wherein a porous network is defined in the material that includes a plurality of nanopores having an average cross-sectional dimension of about 800 nanometers or less.