Imaging genetics, one of the foremost emerging topics in the medical imaging field, analyzes the inherent relations between neuroimaging and genetic data. As deep learning has gained widespread acceptance in many applications, pioneering studies employed deep learning frameworks for imaging genetics. However, existing approaches suffer from some limitations. First, they often adopt a simple strategy for joint learning of phenotypic and genotypic features. Second, their findings have not been extended to biomedical applications, e.g., degenerative brain disease diagnosis and cognitive score prediction. Finally, existing studies perform insufficient and inappropriate analyses from the perspective of data science and neuroscience. In this work, we propose a novel deep learning framework to simultaneously tackle the aforementioned issues. Our proposed framework learns to effectively represent the neuroimaging and the genetic data jointly, and achieves state-of-the-art performance when used for Alzheimer's disease and mild cognitive impairment identification. Furthermore, unlike the existing methods, the framework enables learning the relation between imaging phenotypes and genotypes in a nonlinear way without any prior neuroscientific knowledge. To demonstrate the validity of our proposed framework, we conducted experiments on a publicly available dataset and analyzed the results from diverse perspectives. Based on our experimental results, we believe that the proposed framework has immense potential to provide new insights and perspectives in deep learning-based imaging genetics studies.