Ligand-protein interactions are usually studied in complex media that also contain lipids. This is particularly relevant for membrane proteins that are always associated with lipid bilayers, but also for water-soluble proteins studied in in vivo conditions. This work addresses the following two questions: (i) How does the neglect of the lipid bilayer influence the apparent ligand-protein affinity? (ii) How can the intrinsic ligand-protein affinity be obtained? Here we present a framework to quantitatively characterize ligand-protein interactions in complex media for proteins with a single binding site. The apparent affinity obtained when following some often-used approximations is also explored, to establish these approximations' validity limits and to allow the estimation of the true affinities from data reported in literature. It is found that an increase in the ligand lipophilicity or in the volume of the lipid bilayer always leads to a decrease in the apparent ligand-protein affinity, both for water-soluble and for membrane proteins. The only exceptions are very polar ligands (excluded from the lipid bilayer) and ligands whose binding affinity to the protein increases supralinearly with ligand lipophilicity. Finally, this work discusses which are the most relevant parameters to consider when exploring the specificity of membrane proteins.