The potential energy surfaces for the electronic ground state of the HXeCl and HXeF molecules are constructed by using the internally contracted multi-reference configuration interaction with the Davidson correction (icMRCI+Q) method and large basis sets. The stabilities and dissociation barriers are identified from the potential energy surfaces. The three-body dissociation channel is found to be the dominate dissociation channel for HXeCl, while two dissociation channels are possible and competitive for HXeF. Based on the obtained potentials, vibrational energy levels of HXeCl and HXeF are calculated using the Lanczos algorithm. Our theoretical results are in good agreement with the available observed values. Particularly, the calculated fundamental frequency of the H-Xe stretching vibration including the Xe matrix effect of HXeCl is found to be 1666.6 cm-1, which is only 17.6 cm-1 higher than the recently observed value of 1649 cm-1.