Broadband observations in B, V, R, and I have been performed for a sample of 28 galaxies cataloged as blue compact dwarf galaxies (BCDs). Our deep imaging, reaching surface brightness levels of a few percent of the sky brightness, has allowed the detection of underlying emission or low surface brightness features for a substantial fraction of the sample. In this paper we present the first results of the program: deep contour maps in the B band, surface brightness profiles, and color profiles for all the galaxies. The information derived for this sample of galaxies has allowed us to analyze the morphology and the structural components of BCDs. Over 70% of the galaxies show complex profiles that preclude fitting by a single standard law, with extra structure at high to intermediate intensity levels. In 21 galaxies of the sample, an underlying low surface brightness component has been detected.