In this work, we present the results obtained from a multi-wavelength campaign, as well as from the public Swift/BAT, XRT, and UVOT data of GRB 060111B for which a bright optical emission was measured with good temporal resolution during the prompt phase. We identified the host galaxy at R~25 mag; its featureless spectral continuum and brightness, as well as the non-detection of any associated supernova 16 days after the trigger and other independent redshift estimates, converge to z~1-2. From the analysis of the early afterglow SED, we find that non-negligible host galaxy dust extinction, in addition to the Galactic one, affects the observed flux in the optical regime. The extinction-corrected optical-to-gamma-ray spectral energy distribution during the prompt emission shows a flux density ratio $F_{gamma}/F_{opt}$=0.01-0.0001 with spectral index $beta_{gamma,opt}> beta_{gamma}$, strongly suggesting a separate origin of the optical and gamma-ray components. This result is supported by the lack of correlated behavior in the prompt emission light curves observed in the two energy domains. The properties of the prompt optical emission observed during GRB 060111B favor interpretation of this optical light as radiation from the reverse shock in a thick shell limit and in the slow cooling regime. The expected peak flux is consistent with the observed one corrected for the host extinction, likely indicating that the starting time of the TAROT observations is very near to or coincident with the peak time. The estimated fireball initial Lorentz factor is >260-360 at z=1-2, similar to the Lorentz factors obtained from other GRBs. GRB 060111B is a rare, good test case of the reverse shock emission mechanism in both the X-ray and optical energy ranges.
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