We present the results of N-band spectro-interferometric observations of the silicate carbon star Hen 38 (IRAS08002-3803) with the MID-infrared Interferometric instrument (MIDI) at the Very Large Telescope Interferometer (VLTI) of the European Southern Observatory (ESO). Our observations of IRAS08002-3803 with baseline lengths of 39-47 m have spatially resolved the dusty environment of a silicate carbon star for the first time and revealed an unexpected wavelength dependence of the angular size in the N band: the uniform-disk diameter is found to be constant and ∼36 mas (72 R*) between 8 and 10 μm, while it steeply increases longward of 10 μm to reach ∼53 mas (106 R*) at 13 μm. Neither spherical shell models nor axisymmetric disk models consisting of silicate grains alone can simultaneously explain the observed wavelength dependence of the visibility and the spectral energy distribution (SED). We propose that the circumstellar environment of IRAS08002-3803 may consist of two grain species coexisting in the disk: silicate and a second grain species, for which we consider amorphous carbon, large silicate grains, and metallic iron grains. Comparison of the observed visibilities and SED with our models shows that such disk models can fairly - though not entirely satisfactorily - reproduce the observed SED and N-band visibilities. Our MIDI observations and the radiative transfer calculations lend support to the picture where oxygen-rich material around IRAS08002-3803 is stored in a circumbinary disk surrounding the carbon-rich primary star and its putative low-luminosity companion.