Multilingual language models (MLLMs) have achieved remarkable success in various cross-lingual transfer tasks. However, they suffer poor performance in zero-shot low-resource languages, particularly when dealing with longer contexts. Existing research mainly relies on full-model fine-tuning on large parallel datasets to enhance the cross-lingual alignment of MLLMs, which is computationally expensive. In this paper, we propose InteMATs, a novel approach that integrates multilingual adapters trained on texts of different levels of granularity. To achieve this, we curate a multilingual parallel dataset comprising 42 languages to pre-train sentence-level and document-level adapters under the contrastive learning framework. Extensive experiments demonstrate the effectiveness of InteMATs in improving the cross-lingual transfer performance of MLLMs, especially on low-resource languages. Finally, our comprehensive analyses and ablation studies provide a deep understanding of the high-quality representations derived by InteMATs.