Low-voltage surge filters are technologically important for the protection of modern computing and telecommunication systems operating at low voltages. In this context the design and characterization of varistors operating at low voltages constitutes a continuous challenge. In the present investigation, composite materials with the multilayered structure ZnO/glass/ZnO were prepared and characterized by current-voltage, I-V, electrical measurements. It was found that a prerequisite for the composite materials to exhibit non-linear electrical properties is the doping of ZnO crystals with Co2+ cations. Whenever composite materials act as varistors, the breakdown voltage is at ca. 3V and shows negligible dependence on the temperature and the polarity of bias voltage. On the contrary, the quality of the resistor to conductor transition, as measured by its steepness, strongly depends on the polarity of the ZnO crystals. The optimum characteristics of the varistors are obtained when both ZnO crystals have an O-face polarity. Finally, non-linear electrical properties are correlated with the formation of a Bi2O3-like pseudo-phase in the borate glass network.