Rehearsal-based approaches are a mainstay of continual learning (CL). They mitigate the catastrophic forgetting problem by maintaining a small fixed-size buffer with a subset of data from past tasks. While most rehearsal-based approaches exploit the knowledge from buffered past data, little attention is paid to inter-task relationships and to critical task-specific and task-invariant knowledge. By appropriately leveraging inter-task relationships, we propose a novel CL method, named DualHSIC, to boost the performance of existing rehearsal-based methods in a simple yet effective way. DualHSIC consists of two complementary components that stem from the so-called Hilbert Schmidt independence criterion (HSIC): HSIC-Bottleneck for Rehearsal (HBR) lessens the inter-task interference and HSIC Alignment (HA) promotes task-invariant knowledge sharing. Extensive experiments show that DualHSIC can be seamlessly plugged into existing rehearsal-based methods for consistent performance improvements, outperforming recent state-of-the-art regularization-enhanced rehearsal methods.