The analysis of Blonder, Tinkham, and Klapwijk describing the crossover between tunnel junction and metallic contact between a normal and a superconductive electrode is applied to the case of a superconductor with an energy-dependent gap function. Such energy dependence arises in the presence of electron-hole asymmetry and is predicted within the theory of hole superconductivity. We study a tight-binding model where the interface is described by a reduced value of the intersite hopping amplitude and the superconducting gap function has on-site and nearest-neighbor components. The tunneling conductance as function of barrier strength is found to exhibit certain differences with the electron-hole symmetric case: the reflection and transmission coefficients are different for incident electrons and holes, and Andreev reflection processes for both electrons and holes are suppressed even in the limit of vanishing barrier strength. A temperature gradient across the barrier gives rise to a thermoelectric effect of universal sign, whose magnitude depends on the degree of electron-hole asymmetry in the superconductor as well as on the barrier strength. For temperatures close to Tc an analytic form for the thermoelectric voltage for arbitrary barrier strength is found. These results give information on the effect of nonideal tunnel barriers on the predicted thermoelectric effect. The possibility of observing these effects in high-temperature and conventional superconductors, and interpretation of existing experimental findings in light of these results is discussed.