Rigid polyurethane (PUR) foams were reinforced with sugar beet pulp (BP) impregnated with Aminopropylisobutyl-polyhedral oligomeric silsesquioxanes (APIB-POSS). BP filler was incorporated into PUR at different percentages—1, 2, and 5 wt.%. The impact of BP filler on morphology features, mechanical performances, and thermal stability of PUR was examined. The results revealed that the greatest improvement in physico-mechanical properties was observed at lower concentrations (1 and 2 wt.%) of BP filler. For example, when compared with neat PUR foams, the addition of 2 wt.% of BP resulted in the formation of PUR composite foams with increased compressive strength (~12%), greater flexural strength (~12%), and better impact strength (~6%). The results of thermogravimetric analysis (TGA) revealed that, due to the good thermal stability of POSS-impregnated BP filler, the reinforced PUR composite foams were characterized by better thermal stability—for example, by increasing the content of BP filler up to 5 wt.%, the mass residue measured at 600 °C increased from 29.0 to 31.9%. Moreover, the addition of each amount of filler resulted in the improvement of fire resistance of PUR composite foams, which was determined by measuring the value of heat peak release (pHRR), total heat release (THR), total smoke release (TSR), limiting oxygen index (LOI), and the amount of carbon monoxide (CO) and carbon dioxide (CO2) released during the combustion. The greatest improvement was observed for PUR composite foams with 2 wt.% of BP filler. The results presented in the current study indicate that the addition of a proper amount of POSS-impregnated BP filler may be an effective approach to the synthesis of PUR composites with improved physico-mechanical properties. Due to the outstanding properties of PUR composite foams reinforced with POSS-impregnated BP, such developed materials may be successfully used as thermal insulation materials in the building and construction industry.