The rapid development of healthcare information management for 3D digital medical libraries, 3D PACS, and 3D medical diagnosis has addressed the security issues pertaining to medical IT technology. This paper presents multiple watermarking schemes for a healthcare information management system for 3D medical image data for the protection, authentication, indexing, and hiding of diagnosis information. The proposed scheme, which is based on POCS watermarking, embeds a robust watermark for a doctor's digital signature and an information retrieval indexing key to the distribution of vertex curvedness; the scheme also embeds a fragile watermark for diagnosis information and an authentication reference message to the vertex distance difference. The multiple embedding process creates three convex sets for robustness, fragileness, and invisibility and projects the 3D medical image data onto these three convex sets alternately and iteratively. Experimental results confirmed that the proposed scheme has the robustness and fragileness to handle various 3D geometric and mesh modifiers simultaneously.