The structure and dynamics of membranes depend on many external and internal factors that in turn determine their biological functions. One of the widely accepted and studied characteristics of biomembranes is their fluidity. We research a simple system with variable fluidity tweakable via its composition. The addition of cholesterol is employed to increase the order of lipid chains, thus decreasing the membrane fluidity, while melatonin is shown to elevate the chain disorder, thus also the membrane fluidity. We utilize the densitometric measurements to show a shift of studied systems closer or further from the gel-to-fluid phase transition. The structural changes represented by changes to membrane thickness are evaluated from small angle neutron scattering. Finally, we look at the ability of the two additives to control the interactions between membrane and amyloid-beta peptides. Our results suggest that fluidizing effect of melatonin can promote an insertion of peptide within the membrane interior. Intriguingly, the latter structure relates possibly to an Alzheimer's disease preventing mechanism postulated in the case of melatonin.