Magnetoelectric (ME) magnetic field sensors commonly rely on one of the two modulation principles: the nonlinear dependence of magnetostrictive strain on the applied field or the stress-induced change in magnetization susceptibility. While both effects coexist in any ME device, different readout schemes can be chosen to utilize one or the other effect for magnetic field sensing. This work demonstrates that both principles can be simultaneously implemented in a single electrically modulated ME sensor with inductive readout (a converse ME sensor). This mixed modulation approach significantly enhances low-frequency sensitivity while not affecting the sensitivity at higher frequencies. This leads to a nontrivial dependency of the sensor sensitivity on the frequency of the magnetic field to be measured and can effectively decrease the sensor bandwidth by up to an order of magnitude. We show that the contribution of the modulation from the nonlinearity of the magnetostrictive strain to the sensor sensitivity can be changed by applying a magnetic bias field, offering an additional dimension to the design of ME sensors, especially for potential applications in the unshielded environment.