Three new silver(I) complexes [Ag(NO₃)(tia)(H₂O)]_n (Ag1), [Ag(CF₃SO₃)(1,8-naph)]_n (Ag2) and [Ag₂(1,8-naph)₂(H₂O)_1.2](PF₆)₂ (Ag3), where tia is thianthrene and 1,8-naph is 1,8-naphthyridine, were synthesized and structurally characterized by different spectroscopic and electrochemical methods and their crystal structures were determined by single-crystal X-ray diffraction analysis. Their antimicrobial potential was evaluated against four bacterial and three Candida species, and the obtained results revealed that these complexes showed significant activity toward the Gram-positive Staphylococcus aureus, Gram-negative Pseudomonas aeruginosa and the investigated Candida species with minimal inhibitory concentration (MIC) values in the range 1.56–7.81 μg/mL. On the other hand, tia and 1,8-naph ligands were not active against the investigated strains, suggesting that their complexation with Ag(I) ion results in the formation of antimicrobial compounds. Moreover, low toxicity of the complexes was detected by in vivo model Caenorhabditis elegans. The interaction of the complexes with calf thymus DNA (ct-DNA) and bovine serum albumin (BSA) was studied to evaluate their binding affinity towards these biomolecules for possible insights into the mode of antimicrobial activity. The binding affinity of Ag1–3 to BSA was higher than that for DNA, indicating that proteins could be more favorable binding sites for these complexes in comparison to the nucleic acids.