This research presents an in-depth exploration of the electrical and magnetic properties of a Polypyrrole Nanotubes/Magnetite Nanoparticles (PPyM) material embedded in a silicone oil matrix. A key finding of our study is the dual nature of the composite, i.e. it exhibits a behaviour akin to \textit{both} electro- and magnetorheological suspensions. This unique duality is evident in its response to varying electric and magnetic field intensities. Our study focuses on examining the electrical properties of the composite, including its dielectric permittivity and dielectric loss factor. Additionally, we conduct an extensive analysis of its rheological behavior, with a particular emphasis on how its viscosity changes in response to electromagnetic stimuli. This property notably underscores the material's dual-responsive nature. Employing a custom experimental design, we integrate the composite into a passive electrical circuit element subjected to alternating electric fields. This methodological approach allows us to precisely measure the material's response in terms of resistance, capacitance, and charge under different field conditions. Our findings reveal substantial changes in the material's electrical conductivity and rheological characteristics, which are significantly influenced by the intensity of the applied fields. These results enhance the understanding of electro-magnetorheological properties of PPyM-based magnetic composites, and also highlight their potential in applications involving smart materials. The distinct electrical, magnetic and rheological modulation capabilities demonstrated by this composite render it as promising candidate for advanced applications. These include sensory technology, actuation systems, and energy storage solutions.