We briefly present the results of recent experiments of transverse scanning tunneling spectroscopy of homogeneous poly(dG)-poly(dC) DNA molecules and discuss them in the light of theoretical investigation. A semiempirical theoretical model is adopted to describe the transverse tunneling current across a DNA molecule placed between a metallic gold substrate and a metallic STM tip. We show that the main trends in the positions and relative magnitudes of the conductance peaks can be explained by a minimal model of a double tunnel junction with the molecule-electrode couplings and the applied voltage explicitly taken into account.