Hybrid composites were developed by dispersing carbon black (CB) nanoparticles and graphite nanoplatelets (GNPs) at 4-6 and 12-14 wt%, respectively, into rubbery epoxy resin. SEM analysis showed that CB particles improved the dispersion of GNPs in the hybrid composite. The thermal conductivity of 4 wt% CB/14 wt% GNP-15/rubbery epoxy hybrid composite, 0.81 W/m K, is ca. four times higher than that of rubbery epoxy. When silane-functionalised, the fillers reduced the viscosity of the hybrid dispersion and made the hybrid composite highly electrically insulating. Nevertheless, filler functionalisation decreased the composite's thermal conductivity by only 16.6%. Compression testing showed that the hybrid fillers increased the compressive modulus and strength of rubbery epoxy by nearly two and three times, respectively. Overall, the hybrid composites with their thermal paste-type morphology, low viscosity, high compliance, improved thermal conductivity and, when fillers are functionalised, low electrical conductivity makes them promising materials as thermal interface adhesives.