Bioinorganic complexes based on silver nanoparticles coated with lysozyme shell (bioconjugates) and aluminosilicate matrices have been synthesizeed. Layered aluminosilicates with the structure of montmorillonite of grade K10 were used as matrices. Complexes with the silver mass fraction 0.3% (from the chemical analysis data) were obtained through fivefold treatment of the aluminosilicate matrix by a sol of bioconjugates with an average particle size of 18 nm and a thickness of the biological cell of similar to 4 nm. The produced biocomplexes were investigated by the methods of X-ray diffraction, scanning electron microscopy, and UV spectroscopy. The samples' antibacterial activity against Gram-negative (E. coli ML-35p, P. aeruginosa ATCC 27853) and Gram-positive (MRSA ATCC 33591, L. monocytogenes EGD) bacteria has been studied. The presence of the biocomplex activity toward antibiotic-resistant strains E. coli ML-35p and MRSA has been revealed.