In this work, graphene nanoplatelets (GNPs) and carbon nanotubes (CNTs) were introduced individually as reinforcing fillers into the immiscible poly (butylene adipate-co-terephthalate)/high density polyethylene (PBAT/HDPE) blend to fabricate the blend-based nanocomposites. Maleated HDPE (PEgMA) served as compatibilizer for the PBAT/HDPE blend. Morphological results confirmed that the added GNPs and CNTs were mainly dispersed in PBAT matrix. Differential scanning calorimetry results showed that both nanofillers facilitated the nucleation of PBAT and HDPE in the composites. Thermogravimetric analysis revealed that the presence of CNT enhanced thermal stability of the composites than the GNPs. Measurement of rheological properties confirmed the achievement of pseudo-network structure of nanofillers in the composites. The composite formation increased the complex viscosity (η*) values of the blend and higher η* values were observed at higher CNT loadings at all frequencies. Evidently increased (2–3 orders) η* is observed at low-frequency region for 3-phr CNT compared with the blend. The rigidity of the PBAT/HDPE blend increased after the formation of nanocomposites. The electrical resistivity of the blend drastically reduced, by up to 8 orders at 3-phr CNT loading.