Although synthetic cationic polymers represent a promising class of effective antibacterial agents, the molecular mechanisms behind their antimicrobial activity remain poorly understood. To this end, we employ atomic-scale molecular dynamics simulations to explore adsorption of several linear cationic polymers of different chemical structure and protonation (polyallylamine (PAA), polyethylenimine (PEI), polyvinylamine (PVA), and poly-l-lysine (PLL)) on model bacterial membranes (4:1 mixture of zwitterionic phosphatidylethanolamine (PE) and anionic phosphatidylglycerol (PG) lipids). Overall, our findings show that binding of polycations to the anionic membrane surface effectively neutralizes its charge, leading to the reorientation of water molecules close to the lipid/water interface and to the partial release of counterions to the water phase. In certain cases, one has even an overcharging of the membrane, which was shown to be a cooperative effect of polymer charges and lipid counterions. Protonated amine groups of polycations are found to interact preferably with head groups of anionic lipids, giving rise to formation of hydrogen bonds and to a noticeable lateral immobilization of the lipids. While all the above findings are mostly defined by the overall charge of a polymer, we found that the polymer architecture also matters. In particular, PVA and PEI are able to accumulate anionic PG lipids on the membrane surface, leading to lipid segregation. In turn, PLL whose charge twice exceeds charges of PVA/PEI does not induce such lipid segregation due to its considerably less compact architecture and relatively long side chains. We also show that partitioning of a polycation into the lipid/water interface is an interplay between its protonation level (the overall charge) and hydrophobicity of the backbone. Therefore, a possible strategy in creating highly efficient antimicrobial polymeric agents could be in tuning these polycation's properties through proper combination of protonated and hydrophobic blocks.