Using density functional methods within the generalized gradient approximation implemented in the Quantum Espresso codes, we modify the band offset in a single layer of boronitrene by substituting a double line of carbon atoms. This effectively introduces a line of dipoles at the interface. We considered various junctions of this system within the zigzag and armchair orientations. Our results show that the ``zigzag-short'' structure is energetically most stable, with a formation energy of 0.502 eV and with a band offset of 1.51 eV. The ``zigzag-long'' structure has a band offset of 1.99 eV. The armchair structures are nonpolar, while the zigzag-single structures show a charge accumulation for the C-substituted B and charge depletion for the C-substituted N at the junction. Consequently there is no shifting of the bands.