Aims: To improve our understanding of substellar formation, we have performed a compositional and structural study of a brown dwarf disk. Methods: We present the results of photometric, spectroscopic, and imaging observations of 2MASS J04442713+2512164, a young brown dwarf (M 7.25) member of the Taurus association. Our dataset, combined with results from the literature, provides a complete coverage of the spectral energy distribution from the optical range to the millimeter, including the first photometric measurement of a brown dwarf disk at 3.7 mm, and allows us to perform a detailed analysis of the disk properties. Results: The target was known to have a disk. High-resolution optical spectroscopy shows that it is accreting intensely, and powers both a jet and an outflow. The disk structure is similar to what is observed for more massive TTauri stars. Spectral decomposition models of Spitzer/IRS spectra suggest that the mid-infrared emission from the optically thin disk layers is dominated by grains with intermediate sizes (1.5 μm). Crystalline silicates are significantly more abundant in the outer part and/or deeper layers of the disk, implying very efficient mixing and/or additional annealing processes. Submillimeter and millimeter data indicate that most of the disk mass is in large grains (>1 mm).