Investigation of multi-functional carbon-based self-sensing structural materials for structural health monitoring applications is a topic of growing interest. These materials are self-sensing in the sense that they can provide measurable electrical outputs corresponding to physical changes such as strain or induced damage. Nevertheless, the development of an appropriate measurement technique for such materials is yet to be achieved, as many results in the literature suggest that these materials exhibit a drift in their output when measured with direct current (DC) methods. In most of the cases, the electrical output is a resistance and the reported drift is an increase in resistance from the time the measurement starts due to material polarization. Alternating current methods seem more appropriate at eliminating the time drift. However, published results show they are not immune to drift. Moreover, the use of multiple impedance measurement devices (LCR meters) does not allow for the simultaneous multi-channel sampling of multi-sectioned self-sensing materials due to signal crosstalk. The capability to simultaneously monitor multiple sections of self-sensing structural materials is needed to deploy these multi-functional materials for structural health monitoring. Here, a biphasic DC measurement approach with a periodic measure/discharge cycle in the form of a square wave sensing current is used to provide consistent, stable resistance measurements for self-sensing structural materials. DC measurements are made during the measurement region of the square wave while material depolarization is obtained during the discharge region of the periodic signal. The proposed technique is experimentally shown to remove the signal drift in a carbon-based self-sensing cementitious material while providing simultaneous multi-channel measurements of a multi-sectioned self-sensing material. The application of the proposed electrical measurement technique appears promising for real-time utilization of self-sensing materials in structural health monitoring.