Herein we report on the synthesis and molecular structures of six silver(I) mixed-ligand complexes containing a heterocyclic thioamide [4-phenyl-imidazole-2-thione (phimtH) or 2,2,5,5-tetramethyl-imidazolidine-4-thione (tmimdtH)] and a tertiary arylphosphane [triphenylphosphine (PPh3), tri-o-tolylphosphane (totp)] or diphosphane [(1,2-bis(diphenylphosphano)ethane (dppe), bis(2-diphenylphosphano-phenyl)ether (DPEphos) or 4,5-bis(diphenylphosphano)-9,9-dimethylxanthene) (xantphos)]. The interaction of the compounds with calf-thymus DNA (CT DNA), as monitored directly via UV–vis spectroscopy and DNA-viscosity measurements and indirectly via its competition with ethidium bromide for DNA-intercalation sites, is suggested to take place via an intercalative mode. The new complexes show selective significant in vitro antibacterial activity against four bacterial strains. The antiproliferative effects and cytostatic efficacies of the complexes against four human cancer cell lines were evaluated. The best cytostatic and cytotoxic activity was appeared for the complexes bearing the phimtH moiety. In order to explain the described in vitro activity of the complexes, and to approach a possible mechanism of action, molecular docking studies were adopted on the crystal structure of CT DNA, DNA-gyrase, human estrogen receptor alpha and a cell-cycle specific target protein, human cyclin-dependent kinase 6.