By the use of the effective field theory with a probability distribution technique, we apply the transverse Ising model with long-range interactions to study a ferroelectric bilayer system with an antiferroelectric interfacial coupling. We investigate in detail the effects of the long-range interactions on the pyroelectric properties and phase diagram of the system. The effects of the thickness, the interfacial coupling and the temperature on the hysteresis loops are discussed. It is found that the pyroelectric properties of the ferroelectric bilayer will be strongly influenced by the long-range interactions. Moreover, the phase transition temperature will increase with an increase of the long-range interaction.