We study the superlattice minibands produced by the interplay between moire pattern induced by hexagonal BN substrate on graphene layer and the interlayer coupling in bilayer graphene with Bernal stacking (BLG). We compare moire miniband features in BLG, where they are affected by the interlayer asymmetry of BLG-hBN heterostructure and trigonal warping characteristic for electrons in Bernal-stacked bilayers with those found in monolayer graphene.