The sensing properties of CNT-BNNT-CNT heterostructures toward NO2, O-2 and H2O has been theoretically investigated applying first principles density function theory in combination with non-equilibrium Green's function formalism. The core idea is to change the current flow mechanism in CNT to a quantum mechanical tunneling process by introducing BNNT insulating layers within the CNT. The required thickness of BNNT layer to achieve this goal has been calculated. Due to the strong sensitivity of the tunneling current to the barrier height and the influence of adsorbed agent on the position of the band edges in BNNT layer a very high level of sensitivity is expected for the proposed device. The binding energies and current as well as device sensitivity has been calculated for energetically favorable adsorption geometries of NO2, O-2 and H2O molecules on device surface. In general NO2 and O-2 tend to chemically bind to the surface and show higher sensitivity comparing to the weakly bound H2O molecule. In order to increase the selectivity of the proposed device, the application of a vertical electric filed on the BNNT part of the device has been suggested. It has been shown that by collecting the signals at different vertical electric fields a very good selectivity could be expected toward NO2, O-2 and H2O gases.