We present a detailed search and analysis of chemically stratified hybrid (traces of helium and hydrogen) white dwarfs in the Sloan Digital Sky Survey (SDSS). Only one stratified white dwarf, PG 1305-017, was known prior to this analysis. The main objective is to confirm the existence of several new stratified objects. We first describe our new generation of stratified model atmospheres, where a thin hydrogen layer floats in diffusive equilibrium on top of a more massive helium layer. We then present the results of our search for hot (T-eff > 30,000 K) white dwarfs with a hybrid spectral type among the similar to 38,000 white dwarf spectra listed in the SDSS. A total of 51 spectra were retained in our final sample, which we analyze using spectroscopic fits to both chemically homogeneous and stratified model atmospheres. We identify 14 new stratified white dwarfs in the SDSS sample. From these results, we draw several conclusions regarding the physical processes that might explain the presence of helium in the atmospheres of all the stars in our sample.