The acoustical macro-behavior of mineral open-cell foam samples is modeled from microstructure morphology using a three-dimensional idealized periodic unit-cell (3D-PUC). The 3D-PUC is based on a regular arrangement of spheres allowed to interpenetrate during the foaming process. Identification and sizing of the 3D-PUC is made from x-ray computed microtomography and manufacturing process information. In addition, the 3D-PUC used allows to account for two scales of porosity: The interconnected network of bubbles (meso-porosity) and the inter-crystalline porosity of a gypsum matrix (micro-porosity). Transport properties of the micro- and the meso-scales are calculated from first principles, and a hybrid micro-macro method is used to determine the frequency-dependent visco-thermal dissipation properties. Olny and Boutin found that the double porosity theory provides the visco-thermal coupling between the meso- and micro-scales [J. Acoust. Soc. Am. 114, 73-89 (2003)]. Finally, the results are successfully compared with experiments for two different mineral foam samples. The main originality of this work is to maintain a direct link between the microstructure morphology and the acoustical macro-behavior all along the multi-scale modeling process, without any adjusted parameter.