In this work, three different types of sandwich structures were manufactured, each using a Formica sheet (a paper-based sheet) as the skin and perlite/sodium silicate foam as the core, with or without a paper honeycomb. The sandwich structures were fabricated by attaching the Formica sheets on both sides of a paper honeycomb core panel, a perlite/sodium silicate foam core panel, and a perlite/sodium silicate foam-filled honeycomb core panel. The flexural characteristics were studied by a three-point bending test and the thermal conductivity was measured using Lee’s thermal conductivity apparatus. The results demonstrated a significant improvement in flexural properties, including core shear stress, facing stress, bending stress, and energy absorption, when incorporating the paper honeycomb reinforcement. The thermal conductivity and flexural properties of the paper honeycomb reinforced and unreinforced perlite/sodium silicate foam-based sandwich panels were found to be very compatible with existing building materials described in the literature that are used for similar applications. The failure investigation revealed that the sandwiches with paper honeycomb failed prematurely only due to core buckling, while the foam-filled honeycomb core-based sandwiches were able to sustain higher loads while exhibiting material failures such as core shear failure, skin rapture, and delamination. It was found that the foam-filled paper honeycomb sandwich structures can withstand higher bending loads than the foam core-based sandwich structure or the paper-honeycomb-based sandwich structure. These developed sandwiches offer potential as green materials due to the characteristics of their constituent materials and they can provide valuable applications in the thermal insulation of buildings.