Analyses of very accurate CoRoT space photometry, past Johnson V photoelectric photometry and high-resolution echelle spectra led to the determination of improved and consistent fundamental stellar properties of both components of AU Monocerotis. We derived new, accurate ephemerides for both the orbital motion (with a period of ) and the long-term, overall brightness variation (with a period of ) of this strongly interacting Be + G semi-detached binary. It is shown that this long-term variation must be due to attenuation of the total light by some variable circumbinary material. We derived the binary mass ratio MG/MB = 0.17 +/- 0.03 based on the assumption that the G-type secondary fills its Roche lobe and rotates synchronously. Using this value of the mass ratio as well as the radial velocities of the G-star, we obtained a consistent light curve model and improved estimates of the stellar masses, radii, luminosities and effective temperatures. We demonstrate that the observed lines of the B-type primary may not be of photospheric origin. We also discover rapid and periodic light changes visible in the high-quality residual CoRoT light curves. AU Mon is put into perspective by a comparison with known binaries exhibiting long-term cyclic light changes. Based on photometry collected by the CoRoT space mission as well as spectroscopy obtained with the FEROS spectrograph attached to the 2.2-m telescope at European Southern Observatory (ESO), La Silla, Chile, under the ESO Large Programme LP178.D-0361, and with the SOPHIE spectrograph of the Observatoire de Haute-Provence (France). The CoRoT space mission was developed and is operated by the French space agency CNES, with the participation of ESA's RSSD and Science Programmes, Austria, Belgium, Brazil, Germany and Spain. Based on observations collected at the Centro Astronómico Hispano Alemán (CAHA) at Calar Alto, operated jointly by the Max-Planck-Institut für Astronomie and the Instituto de Astrofísica de Andalucía (CSIC). E-mail: maarten.desmet [at] ster.kuleuven.be (maarten[dot]desmet[at]ster[dot]kuleuven[dot]be)