Traditional information diffusion models are significantly limited in their ability to represent network structure and feedback mechanisms. This results in an ineffective model of dynamic and nonlinear information diffusion across different platforms and modalities. To overcome these issues, we propose a non-Markovian, state-reversible, inter-layer coupled, and dynamically adjustable information propagation model named ML-SIRI. It breaks through the traditional SIR-type models' assumptions of "immunity being permanent" and "inter-layer coupling being static", and realizes the nonlinear modeling of cross-platform information propagation from the perspectives of feedback mechanisms and coupling dynamics. Our approach introduces a multilevel framework with dynamic coupling between layers and a 're-infection' state to capture complex interactions. Based on the principles of dynamic systems and heterogeneous user modelling, we define two key parameters: user activity and influence to describe microscopic state transition processes and the coupling between layers. We then formulate the corresponding dynamic equations and coupling strength measures. We validate the model on synthetic multilevel networks and three real-world datasets (Weibo, WeChat and online media) , comparing it with the single-level benchmark models SIR, SEIR and SIRI. The results demonstrate that ML-SIRI significantly outperforms the other models, improving the prediction of diffusion extent by 30%, 24%, and 18%, respectively, and increasing predictive accuracy by 58.2%, 66.1%, and 73.2%, respectively. These results confirm the effectiveness and robustness of ML-SIRI in dealing with complex diffusion scenarios and heterogeneous network structures, providing an advanced tool for analyzing information diffusion in the multi-channel era.