We present and discuss near-infrared broadband and spectrophotometric images (lambda/Delta lambda = 60) of the gravitationally lensed quadruple image of Q2237+0305 obtained with the MONICA camera at the Canada-France-Hawaii Telescope in 1991, 1992, 1993, and 1994. The spectrophotometric observations cover the wavelength range 1700 < lambda (nm) < 2400, which includes the H alpha emission redshifted to 1770 nm. Our results show that microamplification was achromatic from 1992 to 1994 and had similar amplitudes in the H alpha and continuum emission. On the other hand, a comparison of our near-infrared continuum data with visible data from the literature shows a striking wavelength dependence of the relative amplification of components A and B at epoch 1991 September. This provides strong support to the thermal accretion disk model as a source of the UV-visible continuum emission of quasars. The H alpha line profile changed between 1992,and 1994 but, at each epoch, differences in line profile between components are not significant (<5%). Since the time delays between images is less than one day, this sets a limit of <3% per day for profile evolution.