This work introduces a framework to study the network formed by the autonomic component of heart rate variability (cardiac process eta) and the amplitude of the different electroencephalographic waves (brain processes delta, theta, alpha, sigma, beta) during sleep. The framework exploits multivariate linear models to decompose the predictability of any given target process into measures of self-, causal and interaction predictability reflecting respectively the information retained in the process and related to its physiological complexity, the information transferred from the other source processes, and the information modified during the transfer according to redundant or synergistic interaction between the sources. The framework is here applied to the eta, delta, theta, alpha, sigma, beta time series measured from the sleep recordings of eight severe sleep apnoea-hypopnoea syndrome (SAHS) patients studied before and after long-term treatment with continuous positive airway pressure (CPAP) therapy, and 14 healthy controls. Results show that the full and self-predictability of eta, delta and theta decreased significantly in SAHS compared with controls, and were restored with CPAP for delta and theta but not for eta. The causal predictability of eta and delta occurred through significantly redundant source interaction during healthy sleep, which was lost in SAHS and recovered after CPAP. These results indicate that predictability analysis is a viable tool to assess the modifications of complexity and causality of the cerebral and cardiac processes induced by sleep disorders, and to monitor the restoration of the neuroautonomic control of these processes during long-term treatment.