We use existing scaling theories by de Gennes, Brochard, and Ajdari to calculate the apparent viscosity of multilayer blends with weakly entangled interfaces. The lowering of the apparent viscosity with respect to the bulk is a manifestation of interfacial slip. The theoretical predictions are compared with the recent experimental data of Zhao and Macosko. The theory is able to describe a continuous transition from a low-slip regime to a high-slip regime when the bulk rheology is still Newtonian, in agreement with experiments. However, the dependence of the apparent viscosity on the shear rate and layer thicknesses is much stronger than what is observed experimentally. The apparent viscosity is also calculated for dilute polymer emulsions. We modify a theory of Palierne, which is valid in the linear viscoelastic regime for the bulk, to include the effects of interfacial slip. (C) 2004 Wiley Periodicals, Inc.