We investigate the nonequilibrium transport properties of a double quantum-dot system connected in parallel to two leads, including intradot electron-electron interaction. In the absence of interactions, the system supports a bound state in the continuum. This state is revealed as a Fano antiresonance in the transmission when the energy levels of the dots are detuned. Using the Keldysh nonequilibrium Green’s-function formalism, we find that the occurrence of the Fano antiresonance survives in the presence of Coulomb repulsion. We give precise predictions for the experimental detection of bound states in the continuum. First, we calculate the differential conductance as a function of the applied voltage and the dot level detuning and find that crossing points in the diamond structure are revealed as minima due to the transmission antiresonances. Second, we determine the thermoelectric current in response to an applied temperature bias. In the linear regime, quantum interference gives rise to sharp peaks in the thermoelectric conductance. Remarkably, we find interaction-induced strong current nonlinearities for large thermal gradients that may lead to several nontrivial zeros in the thermocurrent. The latter property is especially attractive for thermoelectric applications.