Aims:We study the contradictory magnetic field strength distributions retrieved from independent analyses of spectropolarimetric observations in the near-infrared (1.56 μm) and in the visible (630 nm) spectral ranges in internetwork regions. Methods: To solve this apparent controversy, we present simultaneous and co-spatial 1.56 μm and 630 nm observations of an internetwork area. The properties of the circular and linear polarization signals, as well as the Stokes V area and amplitude asymmetries, are discussed. As a complement, we also used inversion techniques to infer the physical parameters of the solar atmosphere. As a first step, the infrared and visible observations are analysed separately to check their compatibility. Finally, the simultaneous inversion of the two data sets is performed. Results: The magnetic flux densities retrieved from the individual analysis of the infrared and visible data sets are strongly correlated. The polarity of the Stokes V profiles is the same at co-spatial pixels in both wavelength ranges. This indicates that both 1.56 μm and 630 nm observations trace the same magnetic structures on the solar surface. The simultaneous inversion of the two pairs of lines reveals an internetwork full of sub-kG structures that fill only 2% of the resolution element. A correlation is found between the magnetic field strength and the continuum intensity: equipartition fields (B˜ 500 G) tend to be located in dark intergranular lanes, whereas weaker field structures are found inside granules. The most probable unsigned magnetic flux density is 10 Mx/cm^2. The net magnetic flux density in the whole field of view is nearly zero. This means that both polarities cancel out almost exactly in our observed internetwork area.