When compared to unimodal systems, multimodal biometric systems have several advantages, including lower error rate, higher accuracy, and larger population coverage. However, multimodal systems have an increased demand for integrity and privacy because they must store multiple biometric traits associated with each user. In this paper, we present a deep learning framework for feature-level fusion that generates a secure multimodal template from each user's face and iris biometrics. We integrate a deep hashing (binarization) technique into the fusion architecture to generate a robust binary multimodal shared latent representation. Further, we employ a hybrid secure architecture by combining cancelable biometrics with secure sketch techniques and integrate it with a deep hashing framework, which makes it computationally prohibitive to forge a combination of multiple biometrics that pass the authentication. The efficacy of the proposed approach is shown using a multimodal database of face and iris and it is observed that the matching performance is improved due to the fusion of multiple biometrics. Furthermore, the proposed approach also provides cancelability and unlinkability of the templates along with improved privacy of the biometric data. Additionally, we also test the proposed hashing function for an image retrieval application using a benchmark dataset. The main goal of this paper is to develop a method for integrating multimodal fusion, deep hashing, and biometric security, with an emphasis on structural data from modalities like face and iris. The proposed approach is in no way a general biometric security framework that can be applied to all biometric modalities, as further research is needed to extend the proposed framework to other unconstrained biometric modalities.