In the present work, two quasi-molecular compounds each involving one antiproton and one electron (p^-), He^+-p^- and H-p^-⁠, are investigated. Using completely relativistic calculations within the finite-basis method adapted to systems with axial symmetry, the adiabatic potential curves are constructed by numerically solving the two-center Dirac equation. The binding energies of electron are obtained as a function of the inter-nuclear distance and compared with the corresponding nonrelativistic values and relativistic leading-order corrections calculated in the framework of other approaches. A semantic analysis of antiproton quasi-molecular ions with compounds containing a proton (p) instead of an antiproton is given. The advantages of the A-DKB method are demonstrated.