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Large-scale cross-lingual language models (LM), such as mBERT, Unicoder and XLM, have achieved great success in cross-lingual representation learning. However, when applied to zero-shot cross-lingual transfer tasks, most existing methods use only single-language input for LM finetuning, without leveraging the intrinsic cross-lingual alignment between different languages that proves essential for multilingual tasks. In this paper, we propose FILTER, an enhanced fusion method that takes cross-lingual data as input for XLM finetuning. Specifically, FILTER first encodes text input in the source language and its translation in the target language independently in the shallow layers, then performs cross-language fusion to extract multilingual knowledge in the intermediate layers, and finally performs further language-specific encoding. During inference, the model makes predictions based on the text input in the target language and its translation in the source language. For simple tasks such as classification, translated text in the target language shares the same label as the source language. However, this shared label becomes less accurate or even unavailable for more complex tasks such as question answering, NER and POS tagging. To tackle this issue, we further propose an additional KL-divergence self-teaching loss for model training, based on auto-generated soft pseudo-labels for translated text in the target language. Extensive experiments demonstrate that FILTER achieves new state of the art on two challenging multilingual multi-task benchmarks, XTREME and XGLUE.