A modified version of the Leary-Henderson-Williams equilibrium thermodynamic theory is used to predict microstructural properties for tapered poly(styrene-butadiene) diblock copolymers containing a random copolymer between the blocks. The interphase thickness, interphase volume fraction, and repeat distance are all predicted to increase as the volume fraction of the added random copolymer increases, whereas the microphase-separation temperature is shown to decrease. Comparison of model results with experimental data for tapered poly(styrene-isoprene) diblock copolymers reveals good agreement for small amounts of the additional random copolymer (up to about 20 vol%). Trends indicate that, at large fractions of random copolymer, the tapered block copolymer may be in a homogeneous state when the nontapered block copolymer would be phase separated under the same conditions.