We present a neutron reflectivity study of the internal structure of multilayers made of a weak polyelectrolyte and a neutral component where interactions between adjacent layers are controlled by hydrogen-bonding. We found the degree of interpenetration of polymer layers expressed as the interlayer roughness to be strongly correlated with the strength of intermolecular interactions between the adjacent layers. In addition, polymer layers become more diffuse with a distance from the substrate. Our results demonstrate that hydrogen-bonded films exhibit a close correlation between their structure and properties, which is essential for various applications.