This paper presents a new secure multiple text and image watermarking scheme on cover eye image using fusion of discrete wavelet transforms (DWT) and singular value decomposition (SVD) for Teleophthalmology. Secure Hash Algorithm (SHA-512) is used for generating hash corresponding to iris part of the cover digital eye image and this unique hash parameter is used for enhancing the security feature of the proposed watermarking technique. Simultaneous embedding of four different watermarks (i.e. Signature, index, caption and reference watermark) in form of image and text using fusion of discrete wavelet transforms (DWT) and singular value decomposition (SVD) is achieved in this paper. The suggested technique initially divides the digital eye image into Region of interest (ROI) containing iris and Non-Region of interest (NROI) part where the text and image watermarks are embedded into the Non-Region of interest (NROI) part of the DWT cover image. The selection of DWT decomposition level for embedding the text and image watermarks depends on size, different characteristics and robustness requirements of medical watermark. The performance in terms of Normalized Correlation (NC) and bit error rate (BER) of the developed scheme is evaluated and analyzed against known signal processing attacks and `Checkmark' attacks. The method is found to be robust against all the considered attacks. The proposed multilevel watermarking method correctly extracts the embedded watermarks without error and is robust against the all considered attacks without significant degradation of the medical image quality of the watermarked image. Therefore the proposed method may find potential application in secure and compact medical data transmission for teleophthalmology applications.