Permanent and transition dipole moments have been calculated for various states of CaF and CaCl by using an effective one-electron variational eigenchannel R-matrix approach combined with generalized quantum defect theory. The ion core dipole moment has been evaluated ab initio. The calculations reproduce the existing measurements involving the lowest states of these compounds to within about 5%. The calculations yield for the first time electronic one-photon transition moments for excitation of the higher Rydberg series members, from the A (2)Pi, C (2)Pi or D (2)Sigma (+) intermediate states. Permanent dipole moments for the higher Rydberg states have also been evaluated. It is found that the dipolar ion core causes an "internal" Stark effect to appear, such that certain series are characterized by strong positive dipole moments and other series are characterized by strong negative dipole moments.