Significant slip can occur in the flow of a blend of two immiscible polymers due to reduced entanglements at their interface. The slip is of practical importance because of its effect on morphology and adhesion in, for example, disordered two-phase blends or multilayer films. Interfacial slip was quantified using two polymer pairs each with closely matched viscosity and elasticity but different miscibility (chi): polypropylene (PP)/polystyrene (PS) chi=0.04 and polyethylene (PE)/fluoropolymer (FP) chi congruent to 0.1. To control the amount of interfacial area, we prepared alternating layers by coextrusion. The number of layers of PP/PS ranged from 20 to 640 while that for PE/FP was 80. Nominal viscosity of the multilayer samples was measured with three types of rheometers: an in-line slit-die rheometer, rotational parallel-disks, and sliding plate. Good agreement was found between the three methods. The nominal viscosity as well as shear normal stresses of the multilayer samples decreased with the number of layers. From the viscosity reduction, an apparent interfacial slip velocity V-slip was calculated. The detectable slip, about 1 mu m/s, occurred at the same level of stress normalized by average plateau modulus tau/G(N,av)(0)=0.01 for both pairs. However, V-slip did not show a sudden increase at a critical shear stress as predicted by Brochard-Wyart and de Gennes [C. R. Acad. Sci., Ser. II: Mec., Phys., Chim., Sci. Terre Univers 317, 13 (1993)] but rather increased V-slip proportional to tau(n), where n approximate to 3 for PS/PP and n approximate to 6 for PE/FP. The steeper dependence of slip on stress for PE/FP may be related to its higher chi value and with its narrower molecular weight distribution.