Hydrophobins are a family of small-sized proteins featuring a distinct hydrophobic patch on the protein's surface, rendering them amphiphilic. This particularity allows hydrophobins to self-assemble into monolayers at any hydrophilic/hydrophobic interface. Moreover, stable pure protein bilayers can be created from two interfacial hydrophobin monolayers by contacting either their hydrophobic or their hydrophilic sides. In this study, this is achieved via a microfluidic approach, in which also the bilayers' adhesion energy can be determined. This enables us to study the origin of the adhesion of hydrophobic and hydrophilic core bilayers made from the class II hydrophobins HFBI and HFBII. Using different fluid media in this setup and introducing genetically modified variants of the HFBI molecule, the different force contributions to the adhesion of the bilayer sheets are studied. It was found that in the hydrophilic contact situation, the adhesive interaction was higher than that in the hydrophobic contact situation and could be even enhanced by reducing the contributions of electrostatic interactions. This effect indicates that the van der Waals interaction is the dominant contribution that explains the stability of the observed bilayers.