Multi-instance partial-label learning (MIPL) is an emerging learning framework where each training sample is represented as a multi-instance bag associated with a candidate label set. Existing MIPL algorithms often overlook the margins for attention scores and predicted probabilities, leading to suboptimal generalization performance. A critical issue with these algorithms is that the highest prediction probability of the classifier may appear on a non-candidate label. In this paper, we propose an algorithm named MIPLMA, i.e., Multi-Instance Partial-Label learning with dual Margin Adjustment, which adjusts the margins for attention scores and predicted probabilities. We introduce a margin-aware attention mechanism to dynamically adjust the margins for attention scores and propose a margin-compliant loss to constrain the margins between the predicted probabilities on candidate and non-candidate label sets. Experimental results on benchmark and real-world datasets demonstrate the superior performance of MIPLMA over existing MIPL algorithms, as well as other well-established multi-instance learning algorithms and partial-label learning algorithms. The source code of MIPLMA is included in the supplementary material and will be publicly accessible.