This paper reports on the synthesis and structure elucidation of track-etched membranes (TeMs) with electrolessly deposited copper microtubes (prepared in etched-only and oxidized polyethylene terephthalate (PET) TeMs), as well as on the comparative testing of arsenic (III) ion removal capacities through bath adsorption experiments. The structure and composition of composites were investigated by X-ray diffraction technique and scanning electron and atomic force microscopies. It was determined that adsorption followed pseudo-second-order kinetics, and the adsorption rate constants were calculated. A comparative study of the applicability of the adsorption models of Langmuir, Freundlich, and Dubinin-Radushkevich was carried out in order to describe the experimental isotherms of the prepared composite TeMs. The constants and parameters of all of the above equations were determined. By comparing the regression coefficients R-2, it was shown that the Freundlich model describes the experimental data on the adsorption of arsenic through the studied samples better than others. Free energy of As(III) adsorption on the samples was determined using the Dubinin-Radushkevich isotherm model and was found to be 17.2 and 31.6 kJ/mol for Cu/PET and Cu/Ox_PET samples, respectively. The high E-Dr value observed for the Cu/Ox_PET composite indicates that the interaction between the adsorbate and the composite is based on chemisorption.