We fabricate hybrid magnetoactive materials (hMAMs) based on cotton fibers, silicone oil, carbonyl iron and graphene nanoplatelets (nGr) at various mass concentrations ΦnGr. The obtained materials are used as dielectric materials for manufacturing plane electrical capacitors. The equivalent electrical capacitance Cp and resistance Rp are measured in an electric field of medium frequency f, without and respectively with a magnetic field of magnetic flux density B in the range from 0.1 T up to 0.5 T. The results are used to extract the components ϵr' and ϵr″ of the complex relative permittivity ϵr*, and to reveal the magnitude of the induced magnetoelectric couplings kx and magnetodielectric effects MDE. It is shown that ϵr', ϵr″, kx and MDE are significantly influenced by f,B and ΦnGr. We describe the underlying physical mechanisms in the framework of dipolar approximation and using elements of dielectric theory. The tunable magnetoelectric and magnetodielectric properties of hMAMs are useful for manufacturing electrical devices for electromagnetic shielding of living organisms.