Modulated thermoreflectance microscopy is applied to the simultaneous determination of the thermal boundary resistances and diffusivities of thin YBaCuO superconducting films deposited on ZrO2, LaAlO3, or SrTiO3 substrates. A rigorous thermal diffusion model is used to fit the observed dependences of the thermoreflectance signal amplitude and phase on the separation between the heating and probe laser spots. Measurements are performed at four to six different modulation frequencies covering an appropriate range. The values of three thermal parameters, namely: the thermal diffusivities of the film and of the substrate, and the thermal resistance at the film/substrate interface, are extracted from a least square fit performed at all these frequencies. The magnitude of the thermal anisotropy of the YBaCuO films is also simultaneously estimated from the amplitude behavior, the ratio D-ab/D-c of the two principal diffusivities turns out to be similar to 4. With this anisotropy value, the measured in-plane thermal diffusivity of YBaCuO films is 2.9-3.6 mm(2)/s, and the film/substrate resistances are 0.8-1.3 x 10(-7) m(2) K/W on the three substrates. The diffusivities measured for the substrates are 1.0 mm(2)/s (ZrO2), 4.1 mm(2)/s (LaAlO3), and 3.3 mm(2)/s (SrTiO3), respectively.