Microwave devices as circulators or tunable filters demand nowadays small size and broad bandwidth. Ferromagnetic nanowired membranes are ideal candidates for this purpose. This paper focuses on the dielectric properties of such substrates, as influenced by the ferromagnetic nature of nanowires and their filling factor. Two particular cases are considered: a membrane filled up to its top with nanowires, forming a one-layer substrate, and a membrane filled up to a certain percentage of its height with nanowires, forming a two-layer substrate. The models proposed in this paper for each case take the inductive and gyromagnetic effects in the wires into account. They predict for the one-layer case a magnetodielectric behavior which is tunable by applying an external magnetic field. The effect is no longer visible for the two-layer topology corresponding to microwave circuit applications.