Non-linear rheology of a mixture of two viscoelastic immiscible liquids undergoing high deformation flow was considered. Using Grmela's formalism (Grmela 1986, 1989, 1993a, b) and the coarse grained picture given by Onuki (1987) and Doi and Ohta (1991), we have derived a set of highly nonlinear time-dependent transport equations that take into account a direct coupling between the rheology and morphology. Breakup, coalescence, and the high deformation of the interface were considered. Models of Doi and Ohta (1991), Lee and Park (1994), and Grmela et al. (1998) are recovered as special cases. The parameters of the model were given a physical meaning in both shear and elongational flows and the predictions of the model were compared to the predictions of the previous models on the basis of experimental results obtained on two model blends PDM/PB polydimethylsiloxane/poly(1-butene)and PP/PS polypropylene/polystyrene blends.