We present the results from an analysis of surface photometry of B, R, and Halpha images of a total of 114 nearby galaxies drawn from the Palomar/Las Campanas Imaging Atlas of Blue Compact Dwarf galaxies. Surface brightness and color profiles for the complete sample have been obtained. We determine the exponential and Sersic profiles that best fit the surface brightness distribution of the underlying stellar population detected in these galaxies. We also compute the (B-R) color and total absolute magnitude of the underlying stellar population and compared them to the integrated properties of the galaxies in the sample. Our analysis shows that the (B-R) color of the underlying population is systematically redder than the integrated color, except in those galaxies where the integrated colors are strongly contaminated by line and nebular-continuum emission. We also find that galaxies with relatively red underlying stellar populations (typically (B-R)>~1mag) show structural properties compatible with those of dwarf elliptical galaxies (i.e. a smooth light distribution, fainter extrapolated central surface brightness and larger scale lengths than BCD galaxies with blue underlying stellar populations). At least ~15% of the galaxies in the sample are compatible with being dwarf elliptical (dE) galaxies experiencing a burst of star formation. For the remaining BCD galaxies in the sample we do not find any correlation between the recent star formation activity and their structural differences with respect to other types of dwarf galaxies.