We study the phase separation configurations and rotational properties of a mixture of two interacting charged Bose-Einstein condensates subjected to a magnetic field trapped in disc and Corbino geometries. We calculate the ground state energies of the azimuthal and radial phase separation configurations using the Gross-Pitaevskii and Thomas-Fermi approximations. We show that the results for the experimentally relevant system parameters of both approaches are in good agreement. For both geometries, an immiscible mixture with equal intracomponent interactions favors azimuthal phase separation for all intercomponent interactions. Only an imbalance in the intracomponent interactions can result in a transition to radial phase separation, for which the transition becomes sensitive to the shape of the trap. We present phase diagrams as functions of the inter- and intracomponent interactions. While radial phase separation is widely favoured in disc geometry, the azimuthal phase separation is favoured for narrower Corbino geometries. We explore the rotational properties of spatially separated condensates subjected to magnetic fields, studying their angular momenta and velocity fields. The quantization of circulation breaks down for azimuthal phase separation. In this case, the bulk region of the condensate continues to display superfluid flow behaviour, whereas the velocity field shows a rigid body behaviour along the phase boundaries.