The three binary mixtures cyclohexane + benzene, cyclohexanol + phenol, and cyclohexylamine + aniline exhibit qualitatively different vapor-liquid phase behavior, that is, azeotropic with a pressure maximum, azeotropic with a pressure minimum, and zeotropic, respectively. Employing molecular modeling and simulation, the COSMO-SAC model, and a cubic equation of state, the root of these effects is studied on the basis of phase equilibria, excess properties for volume, enthalpy, and Gibbs energy as well as microscopic structure. It is found that cyclohexane + benzene is characterized by more pronounced repulsive interactions, leading to pressure maximum azeotropy and a positive excess Gibbs energy. Functionalizing the aliphatic and aromatic rings with one amine group each introduces attractive hydrogen bonding interactions of moderate strength that counterbalance such that the mixture becomes zeotropic. The hydroxyl groups introduce strong hydrogen bonding interactions, leading to pressure minimum azeotropy and a negative excess Gibbs energy.