While the structural-acoustic coupling between flexible structures and closed acoustic cavities has been extensively studied in the literature, the modeling of structures coupled through open cavities, especially connected in cascade, is still a challenging task for most of the existing methods. The possible presence of micro-perforated panels (MPPs) in such systems adds additional difficulties in terms of both modeling and physical understanding. In this study, a sub-structuring methodology based on the Patch Transfer Function (PTF) approach with a Compound Interface treatment technique, referred to as CI-PTF method, is proposed, for dealing with complex systems involving cascade open/closed acoustic cavities and MPPs. The co-existence of apertures and solid/flexible/micro-perforated panels over a mixed separation interface is characterized using a compound panel subsystem, which enhances the systematic coupling feature of the PTF framework. Using several typical configurations, the versatility and efficiency of the proposed method is illustrated. Numerical studies highlight the physical understanding on the behavior of MPP inside a complex vibroacoustic environment, thus providing guidance for the practical design of such systems.