Although the performance of the medium access control (MAC) of the IEEE 802.15.4 has been investigated under the assumption of ideal wireless channel, the understanding of the cross-layer dynamics between MAC and physical layer is an open problem when the wireless channel exhibits path loss, multi-path fading, and shadowing. The analysis of MAC and wireless channel interaction is essential for consistent performance prediction, correct design and optimization of the protocols. In this paper, a novel approach to analytical modeling of these interactions is proposed. The analysis considers simultaneously a composite channel fading, interference generated by multiple terminals, the effects induced by hidden terminals, and the MAC reduced carrier sensing capabilities. Depending on the MAC parameters and physical layer thresholds, it is shown that the MAC performance indicators over fading channels can be far from those derived under ideal channel assumptions. As novel results, we show to what extent the presence of fading may be beneficial for the overall network performance by reducing the multiple access interference, and how this information can be used for joint selection of MAC and physical layer parameters.