The confined electron-interface (IF) polar optical phonon scattering in double heterostructures is considered within the dielectric continuum approach. The dependences of electron-IF phonon scattering rate (SR) on the quantum well (QW) width and on the IF phonon frequencies are calculated. The intrasubband SR of electrons confined in the QW by IF phonons is estimated for AlAs / GaAs / AlAs, GaAs / InAs / GaAs, and GaN / InN / GaN heterostructures. The SR of electrons, the energy of which is higher than the barrier phonon energy, increases with an increase of the phonon energy. It is shown that the SR of electrons, the energy of which corresponds to the bulk phonon energy in a QW material, by symmetric IF phonons strongly decreases with a decrease of the QW width, when the width is smaller than 5-10 nm. Contrary, the SR of electrons, the energy of which exceeds the highest IF phonon energy, by IF phonons increases in a narrow QW. This means that the electron mobility and the saturated drift velocity at high electric fields in a narrow QW must be higher than in a wide one.