Recent studies have revealed the remarkable cross-lingual capability of multilingual pre-trained language models (mPLMs), even when pre-trained without parallel corpora (mono-mPLMs). Intuitively, semantic alignments may be the reason behind such capability but remain under-explored. In this work, we investigate the alignment properties from the token perspective in mono-mPLMs and find that the alignments correspond to the geometric similarity of embedding space across different languages. Nevertheless, mono-mPLMs tend to damage this geometric similarity at the higher layers due to the lack of cross-lingual interactions, thus limiting their cross-lingual transfer capabilities. To address this issue, we introduce token-level and semantic-level code-switched masked language modeling, employing the self-induced token alignments to explicitly improve cross-lingual interactions over layers of mono-mPLMs without relying on parallel sentences. We evaluate our method on various natural language understanding tasks and unsupervised machine translation tasks. The results demonstrate that our methods outperform the strong baselines and achieve comparable performance with mPLMs trained with parallel corpora.