In this paper, we propose a secure multibiometric system that uses deep neural networks and error-correction coding. We present a feature-level fusion framework to generate a secure multibiometric template from each user's multiple biometrics. Two fusion architectures, fully connected architecture and bilinear architecture, are implemented to develop a robust multibiometric shared representation. The shared representation is used to generate a cancelable biometric template that involves the selection of a different set of reliable and discriminative features for each user. This cancelable template is a binary vector and is passed through an appropriate error-correcting decoder to find a closest codeword and this codeword is hashed to generate the final secure template. The efficacy of the proposed approach is shown using a multimodal database where we achieve state-of-the-art matching performance, along with cancelability and security.