Using the Quantum Monte Carlo (QMC) technique within frozen-phonon, we studied the effects of the half-breathing O$(\pi,0)$ phonon mode on the ground-state properties of the three-band Peierls-Hubbard model. Our simulations are performed for both ionic and covalent electron-phonon couplings. The effects of lattice displacements on the ground-state energies and charge fluctuations are similar in magnitude for both hole- and electron-doped cases. However, the effects of lattice displacements on the magnetic properties are rather different. In the hole-doped case, the normalized next-nearest-neighbor Cu-Cu spin correlations are dramatically modified by both ionic and covalent electron-phonon couplings. On the other hand, in the electron-doped case, much smaller effects are observed. The distinct spin-phonon couplings, in conjunction with the spin-bag picture of the quasiparticle, could explain a strong mass renormalization effect in the p-type cuprates and a weaker effect in the n-type cuprates.