We calculate the finite temperature and nonequilibrium electric current through systems described generically at low energy by a singlet and two spin doublets forN andN±1 electrons, respectively, coupled asymmetrically to two conducting leads, which allows for destructive interference in the conductance. The model is suitable for studying transport in a great variety of systems such as aromatic molecules, different geometries of quantum dots, and rings with applied magnetic flux. As a consequence of the interplay between interference and Kondo effect, we find changes by several orders of magnitude in the values of the conductance and its temperature dependence as the doublet level splitting is changed by some external parameter. The differential conductance at finite bias is negative for some parameters.