To alleviate labeling complexity, in multi-instance multi-label learning, each sample/bag consists of multiple instances and is associated with a set of bag-level labels leaving instances therein unlabeled. This setting is more convenient and natural for representing complicated objects with multiple semantic meanings. Compared to single-instance labeling, this approach allows for labeling larger datasets at an equivalent labeling cost. However, for sufficiently large datasets, labeling all bags may become prohibitively costly. Active learning (AL) uses an iterative labeling and retraining approach to provide reasonable classification performance using a small number of labeled samples. To our knowledge, only two approaches have been previously proposed for AL in the MIML setting. These approaches either require labeling all classes in a selected bag or involve partial instance-level labeling. To further reduce labeling costs, we propose a novel bag-class pair-based approach for AL in the MIML setting. Due to the partial availability of bag-level labels, we focus on AL in the incomplete-label MIML setting. For the query process, we adapt AL criteria to the novel bag-class pair selection strategy. Additionally, we introduce an online approach for learning a discriminative graphical model based classifier. Numerical experiments on benchmark datasets demonstrate the effectiveness of the proposed approach.