A robust nanobiocomposite based on core-shell heterostructured multiwalled carbon nanotubes@reduced graphene oxide nanoribbons (MWCNTs@rGONRs)/chitosan (CHIT) was described for the fabrication of sensitive, selective, reproducible and durable biosensor for hydrogen peroxide (H₂O₂) and nitrite (NO₂⁻). The excellent physicochemical properties of MWCNTs@rGONRs such as, presence of abundant oxygen functionalities, higher area-normalized edge-plane structures and chemically active sites in combination with excellent biocompatibility of CHIT resulting in the versatile immobilization matrix for myoglobin (Mb). The most attractive property of MWCNTs@rGONRs which distinguishes it from other members of graphene family is its rich edge density and edge defects that are highly beneficial for constructing enzymatic biosensors. The direct electron transfer characteristics such as, redox properties, amount of immobilized active Mb, electron transfer efficiency and durability were studied. Being as good immobilization matrix, MWCNTs@rGONRs/CHIT is also an excellent signal amplifier which helped in achieving low detection limits to quantify H₂O₂ (1 nM) and NO₂⁻ (10 nM). The practical feasibility of the biosensor was successfully validated in contact lens cleaning solution and meat sample.