We studied the quiet-Sun magnetic fields interpreting spectro-polarimetric observations of infrared and visible spectral lines. Magnetic field strengths and filling factors were inferred by the simultaneous inversion of Stokes profiles of the Fe I lines at 6301.5, 6302.5, 15648, and 15653 Å under the MISMA hypothesis. They cover a solar intra-network region at disk center. We analyzed Stokes profiles with signals above noise in both spectral ranges, which correspond to 40% of the field of view. Most of these 2280 profiles could only be inverted with a model including 3 magnetic components with very different field strengths, which indicates the co-existence of kG and sub-kG fields. We measured a total unsigned magnetic flux density of 9.6 G over the whole field of view. For half of the pixels the magnetic field has opposite polarities within the resolution element. We computed the probability density function of finding each magnetic field strength. It has an important contribution of kG field strengths, which concentrates most of the magnetic flux and energy. This kG contribution has a preferred magnetic polarity while the weak fields are balanced.