(Abridged) We present a detailed analysis of the morphology, isophotal parameters and surface brightness profiles for 100 early-type members of the Virgo Cluster, from dwarfs (M_B = -15.1 mag) to giants (M_B = -21.8 mag). Each galaxy has been imaged in two filters, closely resembling the Sloan g and z passbands, using the Advanced Camera for Surveys on board the Hubble Space Telescope. Dust and complex morphological structures are common, with kiloparsec-scale stellar disks, bars, and nuclear stellar disks seen in 60% of galaxies with intermediate luminosity (-20 < M_B < -17), and dust seen in 42% of galaxies brighter than M_B = -18.9 mag. Dust morphologies range from faint wisps and patches on tens of parsec scales, to regular, highly organized kpc-scale dust disks, often showing evidence of recent star formation. Surface brightness profiles and isophotal parameters are derived typically within 8 kpc from the center for the brightest galaxies, and 1.5 kpc for the faintest systems, with a resolution (FWHM) of 7 pc. Based on a parametrization of the surface brightness profiles in terms of a Sersic or core-Sersic model, we find that 1) there is no evidence of a bimodal behavior of the slope, gamma, of the profile in the innermost regions; 2) although the brightest galaxies have shallow inner profiles, the shallowest profiles (lowest gamma values) are found in faint dwarf systems; 3) the widely adopted separation of early-type galaxies between core and power-law types, which had originally been prompted by the claim of a clear bimodal distribution of gamma values, is untenable; and 4) there is no evidence of a structural dichothomy between dwarf and regular ellipticals.
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