Measurements on current-biased Nb/AlO(x)/Al/AlO(x)/Nb double tunnel junction devices with very thin central Al layers show a novel double hysteretic structure in the subgap region. Similar junction structures have previously exhibited very large nonequilibrium effects; the effects reported here appear close to and above the equilibrium critical temperature of Al. A model is presented in which the hysteresis is shown to arise from a transition from finite to zero voltage across one barrier on increasing current, due to the nucleation of an inhomogeneous state in the ultrathin central Al layer in which normal and superconducting states coexist. This reverse switching effect is shown to arise from the self-shunting effect of low-gap regions. Predictions of this model are shown to agree with the experimental data.