[Display omitted] • We have investigated the structure and the stability of ternary complexes, consist of an aromatic π-surface, a cation, and an anion. • The nature of interactions and cooperative effects are studied using various analyses such as theory of AIM, NICS, EDA. • Illustrated the interplay between cation···π and anion···π interactions when they coexist in the same system. We have investigated the structure and the stability of ternary complexes, made up of an extended aromatic π-surface that simultaneously interacts with cation and anion on the opposite faces of the aromatic π-cloud. To understand the influence of the role of aromatic surfaces in the ternary complexes, we have considered various linear and circular polycyclic aromatic hydrocarbons (PAHs) as model systems for the extended π-electron surface. The interplay between the structure, stability, and cooperativity is studied using density functional theory (DFT) methods. Furthermore, the nature of the interaction, energetics, and origin of cooperative effects in the ternary complexes are characterized by using atoms in molecules (AIM), nucleus independent chemical shift (NICS), and energy decomposition analyses (EDA). Results obtained from these calculations unravel the cooperative effects present in the ternary complexes and the interplay between cation···π and anion···π interactions when they coexist in the same system. [ABSTRACT FROM AUTHOR]