Metallic gate electrodes are often employed to control the conductivity of graphene based field effect devices. The lack of transparency of such electrodes in many optical applications is a key limiting factor. We demonstrate a working concept of a double layer graphene field effect device that utilizes a thin film of sputtered aluminum nitride as dielectric gate material. For this system, we show that the graphene resistance can be modified by a voltage between the two graphene layers. We study how a second gate voltage applied to the silicon back gate modifies the measured microwave transport data at around 8.7 GHz. As confirmed by numerical simulations based on the Boltzmann equation, this system resembles a parallel circuit of two graphene layers with different intrinsic doping levels. The obtained experimental results indicate that the graphene-aluminum nitride-graphene device concept presents a promising technology platform for terahertz- to- optical devices as well as radio-frequency acoustic devices where piezoelectricity in aluminum nitride can also be exploited.