This study presents the possibility of using diffusion dialysis for the separation of inorganic acids (hydrochloric, nitric, and hydrofluoric) and their ferric salts whose composition corresponds to that of real spent pickling solutions. At a steady state, the transport properties of three different anion-exchange membranes (Fumasep-FAD, Neosepta-AFN, and Neosepta-AHA) are compared using a continuous counter-current dialyzer. At a constant composition of the solutions (acid concentration 3 mol L−1 and iron concentration 30–40 g L−1), the effects of volumetric liquid flow rates on the transport rate of H+ and Fe3+ ions through the membrane are studied. The dialysis process is characterized by the recovery of acids and the rejection of salts. Furthermore, the values of the dialysis coefficients of acids, iron, and the acid/iron separation factors are calculated and compared. The volumetric flow rates of the inlet streams change in limits from 3 × 10−8 to 6 × 10−8 m3 s−1 (from 3 to 6 L h−1 m−2, relative to the membrane area). A comparison of the tested membranes shows slightly better results for acid recovery, iron rejection, and acid/iron separation factors for the Fumasep-FAD membrane than for the Neosepta-AFN membrane. However, the results obtained show that both of these anion-exchange membranes can be considered good separators for tested mixtures that simulate real spent pickling solutions, and there is a good precondition for using diffusion dialysis for processing these solutions in industrial practice. On the contrary, very low values of acid recovery and the overall dialysis coefficient of acid are found for the Neosepta-AHA membrane in the test range of the volumetric flow rate, and, thus, this membrane is insufficient for the adequate separation of these acids and iron salts.