The steady-shear viscosity and first normal stress difference and the dynamic storage and loss moduli have been measured for a blend consisting of a thermotropic liquid crystalline polymer dispersed in a thermoplastic fluoropolymer matrix. The components are immiscible and nonreacting. Consistency with the Palieme emulsion theory for viscoelastic blends is possible if and only if the interfacial tension contribution is negligible for droplets that are comparable in size to a liquid crystalline domain or smaller, while retaining the effect for larger droplets. Steady shear results are approximately described by the scaling of the Doi-Ohta theory, but there is a significant reduction in the excess shear stress over a finite shear-rate range for the lowest concentration, which contains the smallest droplets.