We present a novel platform for investigating the composition-specific interactions of proteins (or other biologically relevant molecules) with model membranes composed of compositionally distinct domains. We focus on the interaction between a mitochondrial-specific lipid, cardiolipin (CL), and a peripheral membrane protein, cytochrome c (cyt c). We engineer vesicles with compositions such that they phase separate into coexisting liquid phases and the lipid of interest, CL, preferentially localizes into one of the domains (the liquid disordered (L-d) phase). The presence of CL-rich and CL-depleted domains within the same vesicle provides a built-in control experiment to simultaneously observe the behavior of two membrane compositions under identical conditions. We find that cyt c binds strongly to CL-rich domains and observe fascinating morphological transitions within these regions of membrane. CL-rich domains start to form small buds and eventually fold up into a collapsed state. We also observe that cyt c can induce a strong attraction between the CL-rich domains of adjacent vesicles as demonstrated by the development of large osculating regions between these domains. Qualitatively similar behavior is observed when other polycationic proteins or polymers of a similar size and net charge are used instead of cyt c. We argue that these striking phenomena can be simply understood by consideration of colloidal forces between the protein and the membrane. We discuss the possible biological implications of our observations in relation to the structure and function of mitochondria.