The task of Detecting and Grounding Multi-Modal Media Manipulation (DGM$^4$) is a branch of misinformation detection. Unlike traditional binary classification, it includes complex subtasks such as forgery content localization and forgery method classification. Consider that existing methods are often limited in performance due to neglecting the erroneous interference caused by unreliable unimodal data and failing to establish comprehensive forgery supervision for mining fine-grained tampering traces. In this paper, we present a Fine-grained Multiple Supervisory (FMS) network, which incorporates modality reliability supervision, unimodal internal supervision and cross-modal supervision to provide comprehensive guidance for DGM$^4$ detection. For modality reliability supervision, we propose the Multimodal Decision Supervised Correction (MDSC) module. It leverages unimodal weak supervision to correct the multi-modal decision-making process. For unimodal internal supervision, we propose the Unimodal Forgery Mining Reinforcement (UFMR) module. It amplifies the disparity between real and fake information within unimodal modality from both feature-level and sample-level perspectives. For cross-modal supervision, we propose the Multimodal Forgery Alignment Reasoning (MFAR) module. It utilizes soft-attention interactions to achieve cross-modal feature perception from both consistency and inconsistency perspectives, where we also design the interaction constraints to ensure the interaction quality. Extensive experiments demonstrate the superior performance of our FMS compared to state-of-the-art methods.