We present a phenomenological theory for the rheological behavior of ordered mesophases of mixed diblock and triblock copolymer under shear. This theory is based on a coupled multilayer model for mesophase dynamics, and represents the extension of an earlier theory [Doi et al., Macromolecules 26, 4935 (1993)] for pure diblock copolymer mesophases. We show that added triblock copolymer suppresses yielding behavior in copolymer mesophases. We discuss the possible relevance of our model to experimental rheological and structural studies of microphase-separated diblock+triblock copolymer solutions in selective solvents.