Water drops dispersed in chloroform and stabilized with phospholipids become adhesive if a bad solvent for lipids, such as silicone oil, is added to the continuous phase. In this way, two sticking drops are separated by a bilayer of phospholipids. By using microfluidic technologies, we probe the stability and properties of such membranes likewise encountered in foams or vesicles. We first establish the stability diagram of adhering drop pairs as a function of the continuous phase composition. We found two regimes of destabilization of the bilayer. The first one concerns a competition between the dynamics of adhesion and the transport of surfactants toward the interfaces that leads to a dilute surfactant coverage. The second one corresponds to a dense surface coverage where the lifetime distribution of the bilayer exponentially decreases as a signature of a nucleation process. In the stable regime, we observe the propagation of adhesion among a concentrated collection of drops. This is another remarkable illustration of the suction consequence when two close deformable objects are pulled apart. Moreover, the present experimental strategy offers a novel way to study the phase diagrams of bilayers from a single phospholipid to a mixture of phospholipids. Indeed, we detect phase transitions at a liquid liquid interface that are ruled by the amount of bad solvent. Finally, we probe the transport of water molecules through the bilayer and show that its permeability is linked to the adhesion energy that reflects its fluidity.