Abstract We have obtained simultaneous and continuous photo-polarization observations of the blazar BL Lacertae in optical and near-infrared (NIR) bands during an historical outburst from 2020 to 2021. In total, 14 nights of observations were performed where 10 observations show microvariability on timescales of a few minutes to several hours. This suggests a compact emission region, and the timescales are difficult to explain by a one-zone shock-in-jet model. Moreover, we found significant differences in the polarization degree (PD) and angle between optical and NIR bands. Nine nights showed a PD in the optical band that is greater than or equal to that in the NIR band, which can be explained by either a shock-in-jet model or the Turbulent Extreme Multi-Zone (TEMZ) model. On the other hand, five nights showed higher PD in an NIR band than an optical band, which cannot be explained by simple shock-in-jet models nor the simple TEMZ model. The observed timescales and wavelength-dependency of the PD and polarization angle suggest the existence of complicated multiple emission regions such as an irregular TEMZ model.