We study light-trapping in thin-film silicon solar cells with rough interfaces. We consider solar cells made of different materials (c-Si and μc-Si) to investigate the role of size and nature (direct/indirect) of the energy band gap in light trapping. By means of rigorous calculations we demonstrate that the Lambertian Limit of absorption can be obtained in a structure with an optimized rough interface. We gain insight into the light trapping mechanisms by analysing the optical properties of rough interfaces in terms of Angular Intensity Distribution (AID) and haze. Finally, we show the benefits of merging ordered and disordered photonic structures for light trapping by studying a hybrid interface, which is a combination of a rough interface and a diffraction grating. This approach gives a significant absorption enhancement for a roughness with a modest size of spatial features, assuring good electrical properties of the interface. All the structures presented in this work are compatible with present-day technologies, giving recent progress in fabrication of thin monocrystalline silicon films and nanoimprint lithography.