Can a periodic unit cell (PUC), whose local characteristic lengths have been identified as governing compressional sound wave properties in solid foams, provide a basis to model their linear elastic properties? How do elastic properties depend on membranes or solid films which may partially close the interconnections between the pores of solid foams? These two questions are the basis of the paper. A positive answer to the first question leads to foam microstructures with a full set of macroscopic parameters entering into the Biot-Allard poroelastic equations, which are critical for the sound insulation problem. Contributing factors such as membrane content, and thickness, are shown to have a significant effect on mechanical properties such as Young's modulus and Poisson ratio. Acoustical properties including sound transmission loss calculations and measurements indicate that this multi-scale approach is a reliable and insofar promising first attempt to bridge the gap between microstructure and the long-wavelength full acoustic properties (visco-inertial, thermal, elastic) of real poroelastic materials.