We study the quiet Sun magnetic fields using spectropolarimetric observations of the infrared and visible Fe I lines at 6301.5, 6302.5, 15648, and 15653 Å. Magnetic field strengths and filling factors are inferred by the simultaneous fit of the observed Stokes profiles under the MISMA hypothesis. The observations cover an intranetwork region at the solar disk center. We analyze 2280 Stokes profiles whose polarization signals are above noise in the two spectral ranges, which correspond to 40% of the field of view. Most of these profiles can be reproduced only with a model atmosphere including three magnetic components with very different field strengths, which indicates the coexistence of kG and sub-kG fields in our 1.5" resolution elements. We measure an unsigned magnetic flux density of 9.6 G considering the full field of view. Half of the pixels present magnetic fields with mixed polarities in the resolution element. The fraction of mixed polarities increases as the polarization weakens. We compute the probability density function of finding each magnetic field strength. It has a significant contribution of kG field strengths, which concentrates most of the observed magnetic flux and energy. This kG contribution has a preferred magnetic polarity, while the polarity of the weak fields is balanced.