  [Abridged] We present deep optical and near-infrared UBVRIHKs imaging data
for 24 blue compact galaxies (BCGs). The sample contains luminous dwarf and
intermediate-mass BCGs which are predominantly metal-poor, although a few have
near-solar metallicities. We have analyzed isophotal and elliptical integration
surface brightness and color profiles, extremely deep (mu_B<29 mag arcsec^{-2})
contour maps and RGB images for each galaxy in the sample. The colors are
compared to different spectral evolutionary models. We detect extremely
extended low surface brightness (LSB) components dominant beyond the Holmberg
radius as well as optical bridges between companion galaxies at the mu_V~28th
mag arcsec^{-2} isophotal level. The central surface brightness mu_0 and scale
length h_r are derived from two radial ranges typically assumed to be dominated
by the underlying host galaxy. We find that mu_0 and h_r of the BCGs host
deviate from those of dwarf ellipticals (dE) and dwarf irregulars (dI) solely
due to a strong burst contribution to the surface brightness profile almost
down to the Holmberg radius. Structural parameters obtained from a fainter
region, mu_B=26-28 mag arcsec^{-2}, are consistent with those of true LSB
galaxies for the starbursting BCGs in our sample, and with dEs and dIs for the
BCGs with less vigorous star formation.
