Photonic materials based on composite films of cellulose nanocrystals (CNCs) and polymers are promising as they can be renewable and show tunable optical and mechanical properties. However, the influence of polymers on CNC self-assembly is not always well understood, and conflicting results are present in the literature. In this study, we incorporate three neutral, water-soluble polymers-poly(ethylene glycol) (PEG), poly(vinyl pyrrolidone) (PVP), and poly(acrylic acid) (PAA)-with different molecular weights into CNC suspensions at various concentrations prior to obtaining iridescent composite thin films by solvent evaporation. Through spectroscopic, potentiometric, and rheological analyses, we find that PVP physically adsorbs to the surface of CNCs resulting in a bathochromic shift in film color with both increasing concentration and polymer molecular weight. In contrast, PEG induces depletion interactions that result in a decrease in the size of chiral nematic CNC domains, with a negligible change in film color. Finally, PAA hydrogen bonds to the hydroxyl groups of CNCs, resulting in a bathochromic color shift along with interesting rheological and liquid-state properties. This work demonstrates a deeper understanding of CNC-polymer interactions during coassembly and formation of iridescent chiral nematic films, allowing for greater control over optical properties of future CNC-based materials.