Multiple types of genomics data are now increasingly available. Existing statistical methods for integrative analysis focus on a common set of samples for which all individual data types are available. However, in practice, certain genomic features are measured in only a small fraction of the entire study population. Eliminating samples that do not overlap across data types can result in substantial information loss. Therefore, we propose a multi-channel fusion framework to efficiently integrate multi-omics data while maximizing information gain. We build upon distributional robust optimization theory and summarize the information from those non-overlapping samples using estimating equations. Our framework makes a relaxed assumption for the underlying outcome generating mechanism and explicitly allows for heterogeneity in the covariate distributions. We anticipate our integrative framework will yield better-calibrated association estimates and improve inference and prediction results.