Electrochemical deposition of aromatic organic molecules by reduction of diazonium reagents enables formation of molecular layers with sufficient integrity for use in molecular electronic junctions of interest to microelectronics. Characterization of organic films with thicknesses in the 1-10 nm range is difficult with Raman spectroscopy, since most molecular structures of electronic interest have Raman cross sections which are too small to observe as either thin films on solid electrodes or within intact molecular junctions. Layer formation on a 10-nm thick Ag island film on a flat carbon surface (eC/Ag) permitted acquisition of structural information using surface enhanced Raman spectroscopy (SERS), in many cases for molecules with weak Raman scattering. Raman spectra obtained on eC/Ag surfaces were indistinguishable from those on carbon without Ag present, and the spectra of oligomeric molecular layers were completely consistent with those of the monomers. Layer growth was predominantly linear for cases where such growth was sterically allowed, and linear growth correlated strongly with the linewidth and splitting of the C=C phenyl ring stretch. Molecular bilayers made by successive reduction of different diazonium reagents were also observable, and will be valuable for applications of 1-20 nm organic films in molecular electronics.