This brief proposes a generalized iterative learning disturbance observer (GILDO) to handle complex disturbances consisting of slowly-varying and multi-periodic components. The observer employs a hierarchical serial-parallel learning structure that incorporates multiple learning channels with distinct time delays and exploits historical information from different periods, thereby enabling simultaneous estimation of both slowly-varying and periodic components. A systematic parameter tuning method is also provided to ease practical implementation. The stability of the observer error system is proven, and the error transfer function is used to characterize the estimation performance at target frequencies and their harmonics. Experimental results on a PMSM drive system demonstrate that the proposed method achieves effective attenuation of speed ripples induced by slowly-varying and periodic disturbances, while retaining a relatively low observer bandwidth.