Encapsulation of chemicals using polymer membranes enables control of their transport and delivery for applications such as agrochemistry or detergency. To rationalize the design of polymer capsules, it is necessary to understand how the membranes' mechanical properties control the transport and release of the cargo. In this article, we use microfluidics to produce model polymer capsules and study in situ their behavior in controlled divergent flows. Our model capsules are obtained by assembling polymer mono and hydrogen-bonded bilayers at the surface of an oil droplet in water. We also use microfluidics to probe in situ the mechanical properties of the membranes in a controlled divergent flow generated by introducing the capsules through a constriction and then in a larger chamber. The deformation and relaxation of the capsules depend on their composition and especially on the molecular interactions between the polymer chains that form the membranes and the anchoring energy of the first layer. We develop a model and perform numerical simulations to extract the main interfacial properties of the capsules from the measurement of their deformations in the microchannels.