Using atomistic molecular dynamics simulations, the role of lipid composition in the interactions of multiple methacrylate antimicrobial polymer agents with model membranes, and the consequent response of the membranes is studied. In our earlier study, methacrylate polymers were observed to induce phase demixing and associated thickness mismatch in a POPE-POPG model microbial membrane. In this work, we probe (1) the role of varying the degree of saturation in lipid acyl chains in the membrane interactions of methacrylate polymers, and (2) whether electrostatics (addition of anionic lipids) can influence the interactions of the polymers with model mammalian membranes. Lipid composition is observed to significantly modify membrane-polymer interactions, leading to differences in both the mode of partitioning and the conformations adopted by the polymers, in addition to impacting membrane properties differently. The results strongly suggest that the oft-cited electrostatic interactions between the antimicrobial agents and the microbial membranes do not fully account for the recognition and subsequent partitioning of the antimicrobial agents. The ability of the methacrylate polymers to sense interfacial lipid packing defects, determined by the PE/PC head groups of lipids, is also found to be influential in their membrane partitioning. Deliberate inclusion of charged anionic lipids into a model mammalian membrane, leading to additional favorable electrostatics, does not reproduce a similar polymer partitioning mechanism to that in its microbial counterpart. The differences observed in the interactions of methacrylate polymers with the various model membranes can be instrumental in extending our understanding of underlying modes of membrane disruption by general antimicrobial agents as well.