This paper focuses on the development of hybrid structures containing two different classes of porous materials, nanocomposite foams made of polyurethane combined with graphene-based materials, and aluminum open-cell foams (Al-OC). Prior to the hybrid structures preparation, the nanocomposite foam formulation was optimized. The optimization consisted of studying the effect of the addition of graphene oxide (GO) and graphene nanoplatelets (GNPs) at different loadings (1.0, 2.5 and 5.0 wt%) during the polyurethane foam (PUF) formation, and their effect on the final nanocomposite properties. Globally, the results showed enhanced mechanical, acoustic and fire-retardant properties of the PUF nanocomposites when compared with pristine PUF. In a later step, the hybrid structure was prepared by embedding the Al-OC foam with the optimized nanocomposite formulation (prepared with 2.5 wt% of GNPs (PUF/GNPs2.5)). The process of filling the pores of the Al-OC was successfully achieved, with the resulting hybrid structure retaining low thermal conductivity values, around 0.038 W∙m⁻¹∙K⁻¹, and presenting an improved sound absorption coefficient, especially for mid to high frequencies, with respect to the individual foams. Furthermore, the new hybrid structure also displayed better mechanical properties (the stress corresponding to 10% of deformation was improved in more than 10 and 1.3 times comparatively to PUF/GNPs2.5 and Al-OC, respectively).