The generation of multi-functional capsules often requires the sequential deposition of different components on the surface of bubbles or drops. Batch-based methods lack fine control over the capsule sizes, including risk of fusion, and cannot ensure identical environments for each capsule. To overcome these issues, different micro/milli-fluidic methods have been developed in the past. However, a major challenge remains in combining an explicit and flexible control over the capsule generation and their residence time in the different solutions within the same device. Using for the first time the example of bubbles covered by layers of oppositely charged polyelectrolytes (PSS/PAH), we introduce an original millifluidic Lab-on-a-Chip device with two novel functions: (1) Size and separation of the bubbles are tuned at constant flow conditions via gas injection through a movible, circular dispense tip into the cross-flow of a rectangular channel. We provide a detailed exploration of the bubbling parameters together with physical justification of the observations. (2) The device exploits gravity to make the generated bubbles rise between horizontally stacked millifluidic chips containing each the controlled flow of a specific polyelectrolyte solution. In analogy with electric circuits, we show how the flow resistance of each chip can be adapted such that bubbles move smoothly between them while avoiding undesired mixing of the solutions. We show first examples of obtained multilayer capsules and discuss their peculiar features, in particular, their outstanding stability with respect to coalescence and dissolution. While our methods use polyelectrolyte assembly on bubbles, they can be readily transferred to other types of solutions or even to drops and particles.