Alzheimer's Disease (AD) is a chronic neurodegenerative disease that severely impacts patients' thinking, memory and behavior. To aid automatic AD diagnoses, many longitudinal learning models have been proposed to predict clinical outcomes and/or disease status, which, though, often fail to consider missing temporal phenotypic records of the patients that can convey valuable information of AD progressions. Another challenge in AD studies is how to integrate heterogeneous genotypic and phenotypic biomarkers to improve diagnosis prediction. To cope with these challenges, in this paper we propose a longitudinal multi-modal method to learn enriched genotypic and phenotypic biomarker representations in the format of fixed-length vectors that can simultaneously capture the baseline neuroimaging measurements of the entire dataset and progressive variations of the varied counts of follow-up measurements over time of every participant from different biomarker sources. The learned global and local projections are aligned by a soft constraint and the structured-sparsity norm is used to uncover the multi-modal structure of heterogeneous biomarker measurements. While the proposed objective is clearly motivated to characterize the progressive information of AD developments, it is a nonsmooth objective that is difficult to efficiently optimize in general. Thus, we derive an efficient iterative algorithm, whose convergence is rigorously guaranteed in mathematics. We have conducted extensive experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) data using one genotypic and two phenotypic biomarkers. Empirical results have demonstrated that the learned enriched biomarker representations are more effective in predicting the outcomes of various cognitive assessments. Moreover, our model has successfully identified disease-relevant biomarkers supported by existing medical findings that additionally warrant the correctness of our method from the clinical perspective.