In the present paper, within the framework of stationary axisymmetric spacetimes, binary systems composed of two unequal co- and counter-rotating extreme Kerr-Newman black holes separated by a massless strut are reported. The metric describing both configurations is introduced in a closed analytical form in terms of five arbitrary parameters: the masses $M_i$, electric charges $Q_i$, and a coordinate distance R. We obtain novel results from these configurations; in particular, those related to the merging process.