Non-acoustic sensors are widely used in speech signal processing tasks, and their immunity to the background acoustic noise shows great benefits to traditional speech enhancement. To avoid using acoustic speech disturbed by strong noise, spectra mapping from throat microphone (TM) speech to acoustic microphone (AM) speech has been studied. However, there is a distinguished difference between the spectra of the two kinds of speech, and the mapping relationship is different in the low-band and high-band spectra, which limits the performance of the traditional full-band spectra mapping model. In this paper, to improve the perceived quality and intelligibility of TM speech, we investigate the low-band and high-band spectral structure between TM and AM speech, respectively, and propose a spectra-based band-division mapping framework for TM speech enhancement based on the investigation. In the framework, the low-band target spectra of AM speech are mapped based on the equalization method, and the high-band spectra are mapped from the full-band TM speech spectra, which are lack of high-frequency components. The overall framework can be viewed as a combination of spectra equalization in the low band and spectra generation in the high band. Both the objective and subjective evaluation results show clear advantages over the existing TM speech enhancement method based on the full-band spectra mapping.