This research presents a new fabrication method for tailoring polymer/carbon nanotubes (CNTs) nanostructures with controlled architecture and composition. The CNTs are finely dispersed in a polymeric latex i.e. polyacrylate, via ultrasonication, followed by a microfiltration process. The later step allows preserving the homogeneous dispersion structure in the resulting solid nanocomposite. The combination of microfiltration and proper choice of the polymer latex allows for the design of complex nanostructures with tunable properties e.g., porosity, mechanical properties. An important attribute of this methodology is the ability to tailor any desired composition of polymer-CNTs systems, i.e., nanotubes content can practically vary anywhere between 0 to 100 wt%. Thus, for the first time a given polymer/CNTs system is studied over the entire CNTs composition, resembling immiscible binary polymer blends. The polymer in these systems exhibits a structural transition from a continuous matrix (nanocomposite) to segregated domains dispersed within a porous CNTs network. An analogy of this structural transition to phase inversion phenomena in immiscible polymer blends is suggested.