While theoretical and experimental efforts have thoroughly addressed microphase-ordered AB diblock copolymer blends with a parent homopolymer (hA or hB) or a second block copolymer, surprisingly few studies have considered comparable ABA triblock copolymers in the presence of hB or an AB diblock copolymer. In this study, we elucidate the roles of additive molecular weight and constraint by examining three matched series of miscible ABA/hB and ABA/AB blends. Self-consistent field theory is employed to analyze molecular characteristics, e.g., segmental distributions, microdomain periods and midblock bridging fractions, as functions of blend composition. Predictions are compared to morphological characteristics discerned by transmission electron microscopy and small-angle X-ray scattering. The corresponding mechanical properties of these blends are measured by dynamic mechanical analysis. The results of this comprehensive work reveal that addition of hB swells the B-lamellae of the ABA copolymer and has a generally deleterious effect on both the dynamic elastic modulus and midblock bridging fraction. In contrast, addition of a lamellar or cylindrical aB copolymer to the same ABA copolymer can promote an increase or decrease in lamellar period and bridging fraction, depending on relative block sizes.