We calculate the electrical conductivity, thermopower, and the electronic contribution to the thermal conductivity of a superlattice, with the electric field and the thermal gradient applied parallel to the interfaces. We include the tunneling between quantum wells. The broadening of the lowest subband when the period of the superlattice is decreased produces a reduction of the thermoelectric figure of merit. However, we found that a moderate increase of the figure of merit may be expected for intermediate values of the period, due to the enhancement of the density of states produced by the superlattice structure.