A twin-screw extruder was used to fabricate poly(butylene succinate) (PBS)/high density polyethylene (HDPE) blends (7:3 weight ratio) and blend-based nanocomposites. Carbon nanotubes (CNTs), graphene nanoplatelets (GNPs) and organoclays (15A and 30B) served as the nanofiller, while maleated HDPE (PEgMA) acted as an efficient compatibilizer for the blend. In the composites, individual nanofillers were mostly localized in HDPE domains, but some fillers were also observed at PBS-HDPE interfaces. The sea-island morphology of compatibilized blend evolved into a pseudo-co-continuous morphology in the composites. Differential scanning calorimetry results confirmed that PEgMA with HDPE evidently accelerated the crystallization of PBS in the blend. The possible nucleation effect of added fillers on PBS crystallization was obscured by the formation of quasi-connected HDPE domains, causing less PBS nucleation sites. The presence of nanofillers improved the thermal stability and burning anti-dripping behavior of the parent blend. The anti-dripping efficiency of added fillers followed the sequence: CNT>15A>30B>GNP. Rigidity of the blend was increased after formation of nanocomposites. In particular, adding GNP resulted in 31% increase in flexural modulus. Development of a pseudo-network structure in the composites was confirmed by measurement of rheological properties. Electrical resistivity of the blend was reduced by more than 6 orders of magnitude at 3 phr CNT loading, demonstrating the achievement of double percolation morphology.