Mylonitic rocks and rock-analogue materials reveal two basic types of structure: (1) a load-bearing framework (LBF) of strong phase contains isolated pockets of weak phase; (2) interconnected layers of weak phase (IWL) separate boudins and clasts of strong phase. Aggregates with the LBF microstructure are characterized by nearly uniform strain rate. Stress is concentrated in the load-bearing framework. In aggregates with an IWL microstructure, strain rate and sometimes also stress are higher in the interconnected weak phase than in the boudins and clasts of strong phase. The degree of stress and strain partitioning depends strongly on the viscous strength contrast and on the relative amounts of the constituent mineral phases. Based on these observations, the rheology of two-phase rock is modelled with separate functions for LBF and IWL microstructures. A new flow law is derived for rock with IWL structure in which two phases undergo dislocation creep. The flow law expresses composite creep strength in terms of temperature, bulk strain rate and the volume proportions and creep parameters of the minerals in the rock. Strain rate and stress are averaged in the constituent phases and slip along phase boundaries maintains strain compatibility within the aggregate. Composite strengths predicted with the IWL flow law fall well within the uniform stress and uniform strain rate bounds and are generally consistent with the viscous strengths of experimentally deformed bimineralic aggregates. A hypothesis of viscous strain energy minimization is used to determine the relative stability of the LBF and IWL microstructures. During steady-state creep, the IWL microstructure is predicted to be stable over a broad range of two-phase compositions and mineral strength contrasts, whereas the LBF microstructure is stable only in rocks with low volume proportions of weak phase and low to moderate mineral strength contrasts. The IWL flow law indicates that rheological stratification in the lithosphere depends strongly on rock composition, especially in rocks with low volume proportions of a weak phase and high mineral strength contrasts.