In quantitative proteomics, mass tag labeling techniques have been widely adopted in mass spectrometry experiments. These techniques allow peptides and proteins from multiple samples of a batch being quantified in a single experiment, and greatly improve the efficiency. However, the batch-processing of samples also results in severe batch effects and non-ignorable missing data occurring at the batch level. Here we developed a multivariate MIxed-effects SElection model framework (mvMISE) to jointly analyze multiple correlated peptides/proteins in labeled proteomics data, considering the batch effects and the non-ignorable missingness. We proposed two different models: to model multiple peptides from the same protein, we employed a factor-analytic random effects structure to characterize the high and similar correlations among peptides; and to model biological dependence among multiple proteins in a functional pathway, we introduced a graphical lasso penalty on the error precision matrix, and implemented an efficient algorithm. We applied the proposed methods to the breast cancer proteomic data from the Clinical Proteomic Tumor Analysis Consortium.