The electronic structure, electrical conductivity, heat capacity and thermal conductivity of BN and BN/graphene/BN with three and five layers are investigated using the tight binding approximation and Green's function method. The BN/graphene/BN trilayers show narrow band gap unlike to BN trilayers where which have wide band gap. The energy gap of BN trilayers decreases linearly with electric field unlike to the BN/graphene/BN trilayers. The magnitude of changes in the band gap for BN trilayers are much higher than the BN/graphene/BN trilayers. The electrical conductivity, heat capacity and thermal conductivity are zero for BN trilayers and it increases with temperature until reaches maximum value then decreases. The electrical conductivity of BN/graphene bilayers is larger than BN bilayers. For all cases, the heat capacity has a Schottky anomalies.
