A good speech model is essential for speech enhancement, but it is very difficult to build because of huge intra- and extra-speaker variation. We present a new speech model for speech enhancement, which is based on statistical models of magnitude-normalized complex spectra of speech signals. Most popular speech enhancement techniques work in the spectrum space, but the large variation of speech strength, even from the same speaker, makes accurate speech modeling very difficult because the magnitude is correlated across all frequency bins. By performing magnitude normalization for each speech frame, we are able to get rid of the magnitude variation and to build a much better speech model with only a small number of Gaussian components. This new speech model is applied to speech enhancement for our previously developed microphone headsets that combine a conventional air microphone with a bone sensor. Much improved results have been obtained.