In the last decade, white-light illuminated Fabry-Pérot interferometers have been established as a widely used, relatively simple, reliable, and cost-effective way to precisely calibrate high-resolution echelle spectrographs. However, a recent study reported a chromatic drift of the Fabry-Pérot interferometer installed at the Habitable-zone Planet Finder (HPF) spectrograph. In particular, they found that the variation of the etalon effective gap size is not achromatic, as has usually been assumed, but that, in fact, it depends on wavelength. Here, we present a similar study of the Espresso Fabry-Pérot interferometer. Using daily calibrations spanning a period of over 2.5 years, we also find clear evidence for a chromatic drift with an amplitude of a few cm/s per day with a characteristic, quasi-oscillatory dependence on wavelength. We conclude that this effect is probably caused by the aging of the dielectric mirror coatings and we expect that similar chromatic drifts might affect all Fabry-Pérot interferometers used for the calibration of astronomical spectrographs. However, we also demonstrate that the chromatic drift can be measured and, in principle, corrected using only standard calibrations based on hollow cathode lamp spectra.