Mesoblends are conveniently generated by sorbing a parent homopolymer into a microphase-separated triblock or higher-order multiblock copolymer swollen by a block-selective solvent. These nonequilibrium systems afford a viable route by which to produce, in systematic fashion, novel copolymer/ homopolymer blends as well as explore homopolymer transport and solubility within a molecularly confined polymer environment. In the present work, we have imbibed poly(ethylene glycol) (PEG) differing in molecular weight into a model poly(styrene-b-ethylene oxide-b-styrene) (SEOS) triblock copolymer and a commercial poly(amide-b-ethylene glycol) (AEG) multiblock copolymer. Solvent quality and solution concentration are found to have a profound effect on PEG solubility in both copolymers, whereas PEG molecular weight over the range 100-4600 is generally less influential. Transmission electron microscopy reveals the spatial distribution of amorphous PEG within the SEOS copolymer matrix, and complementary differential scanning calorimetry establishes the role of added PEG on the thermal behavior of the copolymer midblock. Incorporation of PEG into the AEG copolymer serves to improve the CO2/H-2 selectivity of this material at ambient temperature and low pressure.