A multimodal technique for inspection of microscopic objects by means of wideband optical microscopy, spectral microscopy, and optical coherence microscopy is described, implemented, and tested. The key feature is the spectral selection of light in the output arm of an interferometer with use of the specialized imaging acousto-optical tunable filter. In this filter, two interfering optical beams are diffracted via the same ultrasound wave without destruction of interference image structure. The basic requirements for the acousto-optical tunable filter are defined, and mathematical formulas for calculation of its parameters are derived. Theoretical estimation of the achievable accuracy of the 3D image reconstruction is presented and experimental proofs are given. It is demonstrated that spectral imaging can also be accompanied by measurement of the quantitative reflectance spectra. Examples of inspection of optically transparent and nontransparent samples demonstrate the applicability of the technique.