The adhesion of cubic boron nitride films can be improved considerably by inserting bias-graded interlayers, consisting of layers deposited with step-wise increased bias voltage. A study of the nucleation of the first h-BN layers on the silicon substrate by atomic force microscopy shows that in the case of our inductively coupled plasma CVD process without interlayer the standard nucleation layer nucleates itself in the island mode, which is not the case for the bias-graded adhesion interlayers. However, even if bias-graded interlayers are used, the standard nucleation layer with the h-BN basal planes standing upright is observed on top of the interlayer prior to c-BN formation. A study of the interlayer system by Fourier transform infrared spectroscopy, elastic recoil detection and high resolution transmission electron microscopy shows that the crystalline fraction, the orientation of the nanocrystals, and the density of the interlayer increase with increasing bias voltage. Possible reasons for the improved adhesion are discussed on the basis of these findings.