In this study, nonwoven fabrics, rigid polyurethane foam (RPUF), Basalt woven fabrics, and an aluminum foil film mold are used to produce multi-functional composite sheets with flame-retardant, sound-absorbing, and electromagnetic-shielding functions. The nonwoven layer is composed of Nomex fibers, flame-retardant PET fibers, and low-melting-point (LMPET) fibers via the needle rolling process. The optimal Nomex fiber/flame-retardant PET fiber/LMPET fiber (N/F/L) nonwoven fabrics are then combined with rigid polyurethane (PU) foam, Basalt woven fabric, and an aluminum foil film mold, thereby producing nonwoven/rigid polyurethane foam/Basalt woven fabric composite sheets that are wrapped in the aluminized foil film. The test results indicate that formed with a foaming density of 60 kg/m3 and 10 wt% of a flame retardant, the composite sheets exhibit electromagnetic interference shielding efficacy (EMI SE) that exceeds 40 dB and limiting oxygen index (LOI) that is greater than 26. The efficient and highly reproducible experimental design proposed in this study can produce multifunctional composite sheets that feature excellent combustion resistance, sound absorption, and EMI SE and are suitable for use in the transportation, industrial factories, and building wall fields.