Molecular-level insight into the interactions of phospholipid molecules with cellulose is crucial for the development of novel cellulose-based materials for wound dressing. Here we employ the state-of-the-art computer simulations to unlock for the first time the molecular mechanisms behind such interactions. To this end, we performed a series of atomic-scale molecular dynamics simulations of phospholipid bilayers on a crystalline cellulose support at various hydration levels of the bilayer leaflets next to the cellulose surface. Our findings clearly demonstrate the existence of strong interactions between polar lipid head groups and the hydrophilic surface of a cellulose crystal. We identified two major types of interactions between phospholipid molecules and cellulose chains: (i) direct attractive interactions between lipid choline groups and oxygens of hydroxyl (hydroxymethyl) groups of cellulose and (ii) hydrogen bonding between phosphate groups of lipids and cellulose's hydroxymethyl/hydroxyl groups. When the hydration level of the interfacial bilayer/support region is low, these interactions lead to a pronounced asymmetry in the properties of the opposite bilayer leaflets. In particular, the mass density profiles of the proximal leaflets are split into two peaks and lipid head groups become more horizontally oriented with respect to the bilayer surface. Furthermore, the lateral mobility of lipids in the leaflets next to the cellulose surface is found to slow down considerably. Most of these cellulose-induced effects are likely due to hydrogen bonding between lipid phosphate groups and hydroxymethyl/hydroxyl groups of cellulose: the lipid phosphate groups are pulled toward the water/lipid interface due to the formation of hydrogen bonds. Overall, our findings shed light on the molecular details of the interactions between phospholipid bilayers and cellulose nanocrystals and can be used for identifying possible strategies for improving the properties of cellulose-based dressing materials via, e.g., chemical modification of their surface.