Context. The detection of bright optical emission measured with good temporal resolution during the prompt phase of GRB 060111B makes this GRB a rare event that is especially useful for constraining theories of the prompt emission.
Aims. For this reason an extended multi-wavelength campaign was performed to further constrain the physical interpretation of the observations.
Methods. In this work, we present the results obtained from our multi-wavelength campaign, as well as from the public Swift/BAT, XRT, and UVOT data.
Results. We identified the host galaxy at R similar to 25 mag from deep R-band exposures taken 5 months after the trigger. Its featureless spectrum and brightness, as well as the non-detection of any associated supernova 16 days after the trigger, enabled us to constrain the distance scale of GRB 060111B within 0.4 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 temporal properties of the prompt optical emission observed during GRB 060111B and their similarities to other rapidly-observed events favor interpretation of this optical light as radiation from the reverse shock. Observations are in good agreement with theoretical expectations for a thick shell limit in 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 Gamma >= 260-360 at z = 1-2, similar to the Lorentz factors obtained from other GRBs. GRB 060111B is a rare case of a GRB with both a bright, well-observed optical counterpart and a "canonical" early X-ray light curve, thus providing a good test case of the reverse shock emission mechanism in both energy ranges.