Ferroelectric multilayers and superlattices have gained interest for dynamic random access memory (DRAM) applications and as active elements in tunable microwave devices in the telecommunications industry. A number of experimental studies have shown that these materials have many peculiar properties which cannot be described by a simple series connection of the individual layers that make up the heterostructures. A thermodynamic analysis is presented to demonstrate that ferroelectric multilayers interact through internal elastic, electrical, and electromechanical fields and the strength of the coupling can be quantitatively described using Landau theory of phase transformations, theory of elasticity, and principles of electrostatics. The theoretical analysis shows that compositional variations across ferroelectric bilayers result in a broken spatial inversion symmetry that can lead to asymmetric thermodynamic potentials favoring one ferroelectric ground state over the other. Furthermore, the thermodynamic modeling indicates that there is a strong electrostatic coupling between the layers that leads to the suppression of ferroelectricity at a critical paraelectric layer thickness for ferroelectric-paraelectric bilayers. This bilayer is expected to have a gigantic dielectric response similar to the dielectric anomaly near Curie-Weiss temperature in homogeneous ferroelectrics at this critical thickness.