The structures of ternary blends composed of a nearly symmetric poly(styrene-b-isoprene-b-dimethylsiloxane) (SID) triblock copolymer (volume fractions of S/I/D = 0.20/0.59/0.21, Mn = 40 000 g/mol) and equal volume fractions of low-molecular-weight polystyrene (Mn = 2360 g/mol) and poly(dimethylsiloxane) (Mn = 2200 g/mol) are investigated by small-angle X-ray and neutron scattering and transmission electron microscopy. When the total homopolymer volume fraction exceeds 65%, the blend macroscopically separates into ordered homopolymer-poor and -rich regions. Between 45 and 65% homopolymer volume fraction, hexagonally packed core-shell cylinders form with PDMS cores and PI shells. Between 15 and 45% homopolymer volume fraction, a core-shell gyroid morphology is observed with PDMS cores and PI shells. These core-shell variations of the classical structures of diblock copolymers are attributed to a small asymmetry in segment-segment interaction parameters. The neat SID block copolymer has a new complex ordered microstructure.