We present a parallel implementation of a large-scale relativistic double-group configuration interaction (CI) program. It is applicable with a large variety of two- and four-component Hamiltonians. The parallel algorithm is based on a distributed data model in combination with a static load balancing scheme. The excellent scalability of our parallelization scheme is demonstrated in large-scale four-component multireference CI (MRCI) benchmark tests on two of the most common computer architectures, and we also discuss hardware-dependent aspects with respect to possible speedup limitations. With the new code we have been able to calculate accurate spectroscopic properties for the ground state and the first excited state of the BiH molecule using extensive basis sets. We focused, in particular, on an accurate description of the splitting of these two states which is caused by spin-orbit coupling. Our largest parallel MRCI calculation thereby comprised an expansion length of 2.7x10(9) Slater determinants.