  (shortened) We analyze deep Near Infrared (NIR) broad band images for a
sample of Blue Compact Dwarf Galaxies (BCDs), allowing for the quantitative
study of their extended stellar low-surface brightness (LSB) host galaxies. NIR
surface brightness profiles (SBPs) of the LSB hosts agree at large
galactocentric radii with those from optical studies. At small to intermediate
radii, however, the NIR data reveal for more than half of our sample a
significant flattening of the exponential SBP of the LSB host. Such SBPs ("type
V" SBPs, Binggeli & Cameron 1991) have rarely been detected in LSB hosts of
BCDs at optical wavelengths, where the relative flux contribution of the
starburst is stronger than in the NIR and can hide such central intensity
depressions of the LSB host. The structural properties, frequency and physical
origin of type V LSB SBPs in BCDs and other dwarf galaxies have not yet been
systematically studied. Nevertheless, their occurrence in a significant
fraction of BCDs would impose important new constraints to the radial
distribution of their stellar mass, and to the photometric fading of BCDs after
the termination of star-forming activity. Both a modified exponential
(Papaderos et al. 1996a) and the Sersic law give satisfactory empirical
descriptions for type V SBPs. However, we argue that the practical
applicability of Sersic fits to LSB SBPs of BCDs is limited by, e.g., the
extreme sensitivity of the solutions to small SBP uncertainties. Most stellar
LSB host galaxies in the sample show optical-NIR colors indicative of evolved
stellar populations with subsolar metallicity. Unsharp-masked NIR images and
optical-NIR maps reveal numerous morphological details, and cases of
non-uniform dust absorption on spatial scales up to ~1 kpc.
