A novel synthesis of polyurethane foam/polyurethane aerogel (PUF–PUA) composites is presented. Three different polyurethane reticulated foams which present the same density but different pore sizes (named S for small, M for medium, and L for large) have been used. After the characterization of the reference materials (either, foams, and pure aerogel), the obtained composites have been characterized in order to study the effect of the foam pore size on the final properties, so that density, shrinkage, porous structure, mechanical properties, and thermal conductivity are determined. A clear influence of the pore size on the density and shrinkage was found, and the lowest densities are those obtained from L composites (123 kg/m3). Moreover, the aerogel density and shrinkage have been significantly reduced through the employment of the polyurethane (PU) foam skeleton. Due to the enhanced mechanical properties of polyurethane aerogels, the inclusion of polyurethane aerogel into the foam skeleton helps to increase the elastic modulus of the foams from 0.03 and 0.08 MPa to 0.85 MPa, while keeping great flexibility and recovery ratios. Moreover, the synthesized PUF–PUA composites show an excellent insulating performance, reducing the initial thermal conductivity values from 34.1, 40.3, and 50.6 mW/(m K) at 10 °C for the foams S, M, and L, to 15.8, 16.6, and 16.1 mW/(m K), respectively. Additionally, the effect of the different heat transfer mechanisms to the total thermal conductivity is herein analyzed by using a theoretical model as well as the influence of the measurement temperature.