In this paper, we propose a novel adaptive soft input soft output (SISO) demodulator that addresses the problem of joint data detection and channel estimation for serially concatenated continuous phase modulation (SCCPM) operating in a time-varying frequency-flat fading channel. Due to its ability of incorporating prior symbol probabilities and its soft output decisions, the proposed SISO demodulator is well suited for serially concatenated CPM systems in attaining better performance through iteration. The bit error rate (BER) results of the proposed iterative receiver and the BER comparison with SISO demodulators based on the per-survivor processing (PSP) and single estimation processing (SEP) methods are presented.