Accurate potential energy curves and molecular constants for the low-lying electronic states of CuX(y) (X = B, Al; y = 0, +1) were investigated using the complete active space self-consistent field/multireference configuration interaction (MRCI) methodology with aug-cc-pV5Z basis set. The photoionization spectra of CuX were computed, showing electron detachment in the region of far ultraviolet. The results complement the previous theoretical characterizations and the few experimental studies. A comparative analysis was carried out concerning the different choices of reference configuration state functions in the MRCI calculations with and without the contribution of scalar relativistic effects. The results obtained with a small reference set adequately constructed are competitive to those using a much larger number of configuration state functions, and also the scalar relativistic effects improve significantly the molecular constants in this kind of system containing a 3d metal atom.