In this paper, rich prosodic information of spontaneous Mandarin speech is explored. The joint prosody labeling and modeling algorithm proposed previously for read speech is extended to spontaneous-speech prosody modeling by additionally considering the modeling of disfluency speech parts. It trains a hierarchical prosodic model and performs prosody labeling from a large speech corpus automatically. Rich prosodic information is then explored via analyzing model parameters and labeling results. By comparing the resulting prosodic model with that of read speech, we find that most affecting patterns, such as F0 contour patterns of 4 tones, have similar shapes or same trends but with much less dynamic ranges. Besides, the prosodic characteristics of various disfluency events, including repetition, restart, repair, contraction, and hesitation, are intensively investigated based on the labeling results. The information explored increases our knowledge about the phonology of spontaneous speech, and should be useful for assisting in ASR.