The development of advanced materials for additive manufacturing has evolved significantly in recent years, driven by the growing demand for lightweight, cost-effective, and sustainable solutions across various industries. Among these, polymer-based foam materials have gained considerable attention due to their unique combination of low density, customizable mechanical properties, and excellent thermal and acoustic insulation capabilities. In the realm of construction and architectural applications, the emergence of printable cementless foam materials offers a versatile and environmentally friendly alternative to traditional cement-based formulations. This study used four industrial by-products, including fly ash, co-fired fly ash, slag, and ultra-fine fly ash, and mixed them as binders to form binary cementless materials. Two polymers (sodium lauryl sulfate and polyvinyl alcohol) were used as foaming agents. Test results revealed that the optimal binary binder was produced by blending 50% ultrafine fly ash with 50% co-fired fly ash. The corresponding water-to-binder ratio was 0.35; the foaming agent combination was 2% sodium lauryl sulfate mixed with 0.3% polyvinyl alcohol (the foaming agent content was 20 wt. % of water). The dry density of the specimens was less than 700 g/cm3, and the thermal conductivity was less than 0.07 W/m.K. The water-to-binder ratio of the specimens was corrected to 0.50 to meet printability requirements. The increase in ultrafine fly ash from 50% to 80% increased the printable height of the specimens from 8 to 20 layers. Besides, the compressive strength was controlled below 1 MPa and the thermal conductivity coefficient was kept below 0.09 W/m.K. In conclusion, this innovative printable binary foam material is suitable for thermal and sound insulation.