We discuss the linear interaction between the de Broglie waves of different electron valleys in heterostructures where a constant electric field is applied along the heterointerfaces (lateral field). The probabilities of phononless and dipole optical transitions of electrons between the Γ- and X-subbands in GaAs/AlAs quantum-well heterosructures with a lateral electric field are calculated. It is shown that the electric field has a strong effect on the probabilities of phononless and direct optical dipole Γ-X electron transitions. Moreover, a lateral electric field changes the spectrum of the intersubband Γ-X light absorption, i.e., there is an intersubband analogue of the Franz-Keldysh effect. The considered linear interaction of de Broglie waves is compared with the well-known cases of linear wave interaction in a magnetized plasma, the Zener breakdown, and the Franz-Keldysh effect in solids.