We develop a theory of the double layer at electrolyte-electrolyte interfaces taking in to account the microscopic structure of the interfacial region. This includes a "mixed boundary layer" where the overlapping of two space-charge regions occurs, and the effects of ion association and adsorption at the interface. Theoretical results are in good agreement with experimental data obtained for various organic solvents and electrolytes. The theory suggests a framework for the treatment of the capacitance data and establishes a relationship between experimental results and the microscopic structure of interfaces between two immiscible electrolyte solutions (ITIES). (C) 2003 Elsevier B.V. All rights reserved.