The miniaturization and integration of next-generation electronic devices are accompanied by a substantial increase in electromagnetic interference (EMI) and heat generation, which requires light and thin EMI shielding materials. Herein, we attempt to tackle this challenge by designing a heterogeneous membrane using carbon nanotubes (CNTs) and magnetite (Fe3O4) nanorods. The polymer-coated Fe3O4 uniformly adsorbs on the surface of the polyaniline (PANi) coated CNTs, forming a self-supporting composite membrane with vertical CNTs under a magnetic field. Due to the entanglement of the CNTs, the vertical alignment is more effective in the top region of the membrane than in the bottom, resulting in an asymmetric structure that is beneficial to EMI absorption. When electromagnetic waves are incident from the top surface, high-absorption electromagnetic shielding is obtained due to multiple attenuations and absorption-reflection losses. The vertical orientation and heterogeneous CNTs network structure of the membrane also enable stable heat dissipation.