Previous work on cross-lingual sequence labeling tasks either requires parallel data or bridges the two languages through word-by-word matching. Such requirements and assumptions are infeasible for most languages, especially for languages with large linguistic distances, e.g., English and Chinese. In this work, we propose a Multilingual Language Model with deep semantic Alignment (MLMA) to generate language-independent representations for cross-lingual sequence labeling. Our methods require only monolingual corpora with no bilingual resources at all and take advantage of deep contextualized representations. Experimental results show that our approach achieves new state-of-the-art NER and POS performance across European languages, and is also effective on distant language pairs such as English and Chinese.