In the field of bottom-up synthetic biology, lipid membranes are the scaffold to create minimal cells and mimic reactions and processes at or across the membrane. In this context, we employ here a versatile microfluidic platform that enables precise positioning of nanoliter droplets with user-specified lipid compositions and in a defined pattern. Adjacent droplets make contact and form a droplet interface bilayer to simulate cellular membranes. Translocation of molecules across membranes are tailored by the addition of alpha-hemolysin to selected droplets. Moreover, we developed a protocol to analyze the translocation of non-fluorescent molecules between droplets with mass spectrometry. Our method is capable of automated formation of one- and two-dimensional droplet networks, which we demonstrated by connecting droplets containing different compound and enzyme solutions to perform translocation experiments and a multistep enzymatic cascade reaction across the droplet network. Our platform opens doors for creating complex artificial systems for bottom-up synthetic biology.