In this work, our goal is to understand the type of molecular-level interactions between NSAIDs and lipid membranes over the entire physiological pH range using both experiments and simulations as an effort to engineer liposomes as effective drug delivery vehicles as a means to safer NSAIDs. Calorimetry experiments on two most common NSAIDs viz. Aspirin and Ibuprofen show that these drugs reduce the gel-liquid transition temperature of zwitterionic phospholipid indicating clearly strong interactions between the drug and lipid over the pH range of 2-10. Molecular dynamics simulations with Dipalmytoyl phosphatidyl choline(DPPC) as model zwitterionic lipid show that the type of drug association varies from strongly non-polar to strongly electrostatic interaction as the pH varies. The effect of different head groups (anionic, cationic etc.) on the drug binding will be highlighted in context of presenting a broader picture of the interactions between the class of NSAIDs with lipid membranes. Finally, simulations for long length and time scales using coarse-grain models built on the basis of molecular-level information obtained from all-atomistic simulations will be presented.