Most previous amplitude- and frequency-modulation (AM and FM) decomposition methods assume that the AM component is non-negative. However this assumption is not always valid. Over-modulation, where the AM component has both positive and negative values, may be present in not only synthetic signals, but also in natural signals like speech and music. Assuming all non-negative values for AM in an over-modulated signal will introduce significant phase discontinuities in the FM estimate. Because of this, previous methods yield significant errors for instantaneous frequency (IF) estimation at AM zero-crossings. We propose a two-step algorithm that utilizes coherent demodulation to estimate AM and FM correctly for over-modulated signals. For synthetic signals, the algorithm produces very accurate AM and FM estimates; for band-passed speech signals, the algorithm corrects the discontinuities in the FM estimate and produces more physically reasonable results. The evaluation of source sensitivity for the algorithm shows that the estimation errors generally increase with AM and FM frequencies, but are insensitive to carrier frequency. The robustness in noise is relatively low in the over-modulation case due to very low local SNR at AM zero-crossings. Limitations of the algorithm and future work are also discussed.