Recent joint models for multi-intent detection and slot filling have obtained promising results through modeling the unidirectional or bidirectional guidance between intent and slot. However, existing works design joint models heuristically and lack some theoretical exploration, including (1) theoretical measurement of the joint-interaction quality; (2) explainability of design and optimization methods of joint models, which may limit the performance and efficiency of designs. In this paper, we mathematically define the cross-task information gain (CIG) to measure the quality of joint processes from an information-theoretic perspective and discover an implicit optimization of CIG in previous models. Based on this, we propose a novel multi-stage iterative framework with theoretical effectiveness, explainability, and convergence, which can explicitly optimize information for cross-task interactions. Further, we devise an information-based joint model (InfoJoint) that conforms to this theoretical framework to gradually reduce the cross-task propagation of erroneous semantics through CIG iterative maximization. Extensive experiment results on two public datasets show that InfoJoint outperforms the state-of-the-art models by a large margin.