We assess the possibility of probing the diffuse electric double layer at a permeable charge-selective interface, such as a nonblocking electrode or ion-exchange membrane, under a finite steady-state current-voltage bias by small harmonic high-frequency current-voltage disturbances. Our main conclusion is that for a finite underlimiting bias, the electric double layer at such an interface is not amenable to this kind of probe; the high-frequency response of the system is dominated by the quasielectroneutral bulk. This is similar to the previously studied zero-bias case. On the other hand, the extended space charge in such double layers may be probed in this way both by the linear and nonlinear responses, correspondingly by the method of electric impedance spectroscopy and via the previously described anomalous rectification effect. The latter appears preferable over the former as a potential experimental tool for the study of the extended space charge of a nonequilibrium electric double layer.