We study the ground state phases of a rotating two-component, or binary, Bose-Einstein condensate, wherein one component possesses a large permanent magnetic dipole moment. A variety of nontrivial phases emerge in this system, including a half-quantum vortex (HQV) chain phase and a HQV molecule phase, where HQVs bind at short distances. We attribute these phases to the development of a minimum in the HQV interaction potential, which emerges without coherent coupling or attractive interactions between the components. Thus, we show that the presence of dipolar interactions in this system provides a unique mechanism for the formation of HQV molecules and results in a rich ground state phase diagram.