Context. Despite observational evidences, InfraRed (IR) excess of classical Cepheids are seldom studied and poorly understood, but probably induces systematics on the Period-Luminosity (PL) relation used in the calibration of the extragalactic distance scale. Aims. This study aims to understand the physical origin of the IR excess found in the spectral energy distribution (SED) of 5 Cepheids : RS Pup (P = 41.46d), ζ Gem (P = 10.15d), η Aql (P = 7.18d), V Cen (P = 5.49d) and SU Cyg (P = 3.85d). Methods. A time series of atmospheric models along the pulsation cycle are fitted to a compilation of data, including optical and near-IR photometry, Spitzer spectra (secured at a specific phase), interferometric angular diameters, effective temperature estimates, and radial velocity measurements. Herschel images in two bands are also analyzed qualitatively. In this fitting process, based on the SPIPS algorithm, a residual is found in the SED, whatever the pulsation phase, and for wavelengths larger than about 1.2µm, which corresponds to the so-determined infrared excess of Cepheids. This IR excess is then corrected from interstellar medium absorption in order to infer or not the presence of dust shells, and is finally used in order to fit a model of a shell of ionized gas. Results. For all Cepheids, we find a continuum IR excess increasing up to ≈-0.1 magnitudes at 30µm, which cannot be explained by a hot or cold dust model of CircumStellar Environment (CSE). However, a weak but significant dust emission at 9.7 µm is found for ζ Gem, η Aql and RS Pup, while clear interstellar clouds are seen in the Herschel images for V Cen and RS Pup. We show, for the first time, that the IR excess of Cepheids can be explained by free-free emission from a thin shell of ionized gas, with a thickness of 15% of the star radius, a mass of 10 −9 − 10 −7 M and a temperature ranging from 3500 to 4500K. Conclusions. The presence of a thin shell of ionized gas around Cepheids has to be tested with interferometers operating in visible, in the mid-IR or in the radio domain. The impact of such CSEs of ionized gas on the PL relation of Cepheids needs also more investigations.A&A proofs: manuscript no. draft_vh_paperI around 3 stellar radii and a flux contribution in the K band, ranging from 2% to 10% of the continuum, for medium-and longperiod Cepheids respectively, while it is around 10% or more in the N band. However, we still do not know how these CSEs are produced, neither their nature, nor their characteristics (density and temperature profiles, chemical composition...).This paper aims at building a phase-dependent Spectral Energy Distribution (SED) of a sample of Cepheids from visible to mid-IR wavelengths and compare it with dedicated atmospheric models in order to quantify and study their IR excess. We present the IR excess of the stars in the sample in Sect. 2 using photometric and Spitzer observations in various bands, and we study qualitatively far-infrared images from Herschel. In Sect. 3 we correct the spectra from interstellar foreground...