  In this paper, we employ the general equatorially symmetric two-soliton
solution of the Einstein-Maxwell equations for elaborating two physically
meaningful configurations describing a pair of equal Kerr-Newman corotating
black holes separated by a massless strut. The first configuration is
characterized by opposite magnetic charges of its constituents, while in the
second configuration the black holes carry equal electric and opposite magnetic
charges, thus providing a nontrivial example of a binary dyonic black-hole
system. The thermodynamic properties of these binary configurations are studied
and the first law of thermodynamics taking correctly into account the magnetic
field contribution is formulated for each case.
