Cells respond to external stress by altering their membrane lipid composition to maintain fluidity, integrity and net charge. However, in interactions with charged nanoparticles (NPs), altering membrane charge could adversely affect its ability to transport ions across the cell membrane. Hence, it is important to understand possible pathways by which cells could alter zwitterionic lipid composition to respond to NPs without compromising membrane integrity and charge. Here, we report in situ synchrotron X-ray reflectivity (XR) measurements to monitor the interaction of cationic NPs in the form of quantum dots, with phase-separated supported lipid bilayers of different compositions containing an anionic lipid and zwitterionic lipids having variable degrees of stiffness. We observe that the extent of NP penetration into the respective membranes, as estimated from XR data analysis, is inversely related to membrane compression moduli, which was tuned by altering the stiffness of the zwitterionic lipid component. For a particular membrane composition with a discernible height difference between ordered and disordered phases, we were able to observe subtle correlations between the extent of charge on the NPs and the specificity to bind to the charged and ordered phase, contrary to that observed earlier for phase-separated model biomembranes containing no charged lipids. Our results provide microscopic insight into the role of membrane rigidity and electrostatics in determining membrane permeation. This can lead to great potential benefits in rational designing of NPs for bioimaging and drug delivery applications as well as in assessing and alleviating cytotoxicity of NPs.