In this work, a multifunctional polymer composite is made using melt-blowing technology from polypropylene (88 wt.%) and poly (ethylene terephthalate) (12 wt.%) with the addition of functional modifiers, that is, 3 g of a superabsorbent polymer and 5 g of a biocidal agent (Biohaloysite). The use of modifiers is aimed at obtaining adequate comfort when using the target respiratory protection equipment (RPE) in terms of microclimate in the breathing zone and protection against harmful aerosols including bioaerosols. The developed production method is innovative in that the two powdered modifiers are simultaneously applied in the stream of elementary polymeric fibers by two independent injection systems. Aerosols of the modifiers are supplied via a specially designed channel in the central segment of the die assembly, reducing the amount of materials used in the production process and saving energy. The results show that the proposed method of incorporating additives into the fiber structure did not adversely affect the protective and functional properties of the resulting filtration nonwovens. The produced nonwoven composites are characterized by SEM, FTIR, and differential scanning calorimetry (DSC). Given their high filtration efficiency at 5%, satisfactory airflow resistance (~200 Pa), very good antimicrobial activity, and excellent water absorption capacity, the obtained multifunctional nonwoven composites may be successfully used in filtering respiratory protective devices.