A novel set of isotropic electromagnetic boundary conditions generalizing some of the recently introduced boundary conditions is introduced. For a planar boundary it is required that the boundary appears as an impedance boundary for the TE and TM components of the field with different surface impedances in the general case. Thus, such conditions can be dubbed as mixed-impedance boundary conditions. It is shown that the conditions can be alternatively expressed in terms of normal components of the fields at the boundary and in this form they can be defined for non-planar boundaries as well. The conditions generalize those of the isotropic impedance boundary and the more recently considered DB and D' B' boundaries. As a numerical example, scattering from a mixed-impedance sphere is considered, and it is found that the sphere could be useful as a cloaking device.