Biological membranes, in addition to being a cell boundary, can host a variety of proteins that are involved in different biological functions, including selective nutrient transport, signal transduction, inter- and intra-cellular communication, and cell-cell recognition. Due to their extreme complexity, there has been an increasing interest in developing model membrane systems of controlled properties based on combinations of polymers and different biomacromolecules, i.e., polymer-based hybrid films. In this review, we have highlighted recent advances in the development and applications of hybrid biomimetic planar systems based on different polymeric species. We have focused in particular on hybrid films based on (i) polyelectrolytes, (ii) polymer brushes, as well as (iii) tethers and cushions formed from synthetic polymers, and (iv) block copolymers and their combinations with biomacromolecules, such as lipids, proteins, enzymes, biopolymers, and chosen nanoparticles. In this respect, multiple approaches to the synthesis, characterization, and processing of such hybrid films have been presented. The review has further exemplified their bioengineering, biomedical, and environmental applications, in dependence on the composition and properties of the respective hybrids. We believed that this comprehensive review would be of interest to both the specialists in the field of biomimicry as well as persons entering the field.