We introduce the use of block copolymer membranes for an emerging application, "drug capture". The polymer is incorporated in a new class of biomedical devices, referred to as ChemoFilter, which is an image-guided temporarily deployable endovascular device designed to increase the efficacy of chemotherapy-based cancer treatment. We show that block copolymer membranes consisting of functional sulfonated polystyrene end blocks and a structural polyethylene middle block (S-SES) are capable of capturing doxorubicin, a chemotherapy drug. We focus on the relationship between morphology of the membrane in the ChemoFilter device and efficacy of doxorubicin capture measured in vitro. Using small-angle X-ray scattering and cryogenic scanning transmission electron microscopy, we discovered that rapid doxorubicin capture is associated with the presence of water-rich channels in the lamellar-forming S-SES membranes in aqueous environment.