The complex hydrophobic and hydrophilic milieus of membrane-associated proteins pose experimental and theoretical challenges to their understanding. Here, we produce a nonredundant database to compute knowledge-based asymmetric cross-membrane potentials from the per-residue distributions of Cβ, Cγ and functional group atoms. We predict transmembrane and peripherally associated regions from genomic sequence and position peptides and protein structures relative to the bilayer (available at http://www.degradolab.org/ez). The pseudo-energy topological landscapes underscore positional stability and functional mechanisms demonstrated here for antimicrobial peptides, transmembrane proteins, and viral fusion proteins. Moreover, experimental effects of point mutations on the relative ratio changes of dual-topology proteins are quantitatively reproduced. The functional group potential and the membrane-exposed residues display the largest energetic changes enabling to detect native-like structures from decoys. Hence, focusing on the uniqueness of membrane-associated proteins and peptides, we quantitatively parameterize their cross-membrane propensity, thus facilitating structural refinement, characterization, prediction, and design. Display omitted ► A statistical potential accurately positions proteins and peptides in the membrane ► Topological energy landscapes present structure-function-stability relationships ► Side-chain functional-atom parameters allow modeling of rotameric preferences ► Experimental effects of point mutations on topology are quantitatively reproduced