Equipment connections in MVDC networks may combine different materials. We consider here the assembly of an epoxy and a silicone rubber composite. As the apparent conductivities of the two materials are highly dependent on temperature, water content and electric field, situations may arise where the voltage applied to the bilayer insulation is mainly applied to one of the two layers, either epoxy or silicone, or is divided over the two sheets. Current densities-voltage (J-V) measurements were carried out on 2 mm thick bilayer samples either at 40°C under three relative humidity conditions (dry, 50% and 90% relative humidity) or under dry conditions at 40, 60 and 80°C. The voltages applied were between 0.25 and 10 kV. These measurements are compared to the currents calculated from measurements made on each monolayer sample under similar T and RH conditions. Under conditions of T and RH where the apparent conductivities of the two materials are very different, as expected, the currents measured in the bilayer samples were close to the currents flowing in the more resistive material. When the currents are of the same order of magnitude, the calculated currents were found to be relevant for evaluating the measured current in the bilayer samples.