The cell membrane is a crucial biological interface to consider in biomedical research, as a significant proportion of drugs interacts with this barrier. While understanding membrane–drug interactions is important, existing in vitro platforms for drug screening predominantly focus on interactions with whole cells or tissues. This preference is partly due to the instability of membrane-based systems and the technical challenges associated with buffer replacement around lipid membranes formed on microfluidic chips. Here, we introduce a novel microfluidic design capable of forming stable freestanding lipid bilayers with efficient replacement of the media in their local environment for molecular delivery to the membrane. With the use of bubble traps and resistance channels, we achieved sufficient hydrodynamic control to maintain membrane stability during the membrane formation and the molecular delivery phases. As a proof of concept, we successfully formed 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine (POPC) bilayers on the chip and delivered the antibiotic azithromycin at low (5 μM) and high (250 μM) doses. Using optical tweezers, we characterized how azithromycin influenced the membrane elastic properties, including tension and bending rigidity. This microfluidic device is a versatile tool that can deliver various buffers, molecules or nano-/microparticles to freestanding membranes, and study the resulting impact on the membranes' properties.