Stokes profiles observed in the quiet photosphere by HINODE SOT/SP present very complex shapes. These are indicative of unresolved magnetic structures and/or gradients along the line of sight in HINODE's pixels which have linear dimension of ˜0.15". We present the first interpretation of the Stokes profile asymmetries measured in the 630 nm Fe I lines by SOT/SP in both quiet Sun internetwork (IN) and network. The inversion is carried out under the hypothesis of MIcro-Structured Magnetized Atmosphere (MISMA) which can account for sub-pixel structuring of magnetic fields. The MISMA code is able to reproduce the observed asymmetries in a very satisfactory way. Moreover, 25% of inverted profiles present asymmetries that are interpreted as produced by regions in which mixed polarities are present. kG field strengths are found in both network and internetwork regions. In the internetwork both kG fields and hG fields are found. Our analysis constrains the magnetic field of only 4.5% of the analyzed photosphere. The rest of the plasma can be thought to be filled by weak fields not contributing to the detected polarization signals.