To address the ever-increasing electromagnetic interference (EMI) pollution, a hybrid filler approach for novel composites was chosen, with a focus on EMI absorbance. Carbon nanofiller loading was limited to 0.6 vol.% in order to create a sustainable and affordable solution. Multiwall carbon nanotubes (MWCNT) and iron oxide (Fe3O4) nanoparticles were mixed in nine ratios from 0.1 to 0.6 vol.% and 8.0 to 12.0 vol.%, respectively. With the addition of surfactant, excellent particle dispersion was achieved (examined with SEM micrographs) in a bio-based and biodegradable poly(butylene succinate) (PBS) matrix. Hybrid design synergy was assessed for EMI shielding using dielectric spectroscopy in the microwave region and transmittance in the terahertz range. The shielding effectiveness (20–52 dB) was dominated by very high absorption at 30 GHz, while in the 0.1 to 1.0 THz range, transmittance was reduced by up to 6 orders of magnitude. Frequency-independent AC electrical conductivity (from 10−2 to 107 Hz) was reached upon adding 0.6 vol.% MWCNT and 10 vol.% Fe3O4, with a value of around 3.1 × 10−2 S/m. Electrical and thermal conductivity were mainly affected by the content of MWCNT filler. The thermal conductivity scaled with the filler content and reached the highest value of 0.309 W/(mK) at 25 °C with the loading of 0.6 vol.% MWCNT and 12 vol.% Fe3O4. The surface resistivity showed an incremental decrease with an increase in MWCNT loading and was almost unaffected by an increase in iron oxide loading. Thermal conductivity was almost independent of temperature in the measured range of 25 to 45 °C. The nanocomposites serve as biodegradable alternatives to commodity plastic-based materials and are promising in the field of electromagnetic applications, especially for EMI shielding.