Recently, token-level adaptive training has achieved promising improvement in machine translation, where the cross-entropy loss function is adjusted by assigning different training weights to different tokens, in order to alleviate the token imbalance problem. However, previous approaches only use static word frequency information in the target language without considering the source language, which is insufficient for bilingual tasks like machine translation. In this paper, we propose a novel bilingual mutual information (BMI) based adaptive objective, which measures the learning difficulty for each target token from the perspective of bilingualism, and assigns an adaptive weight accordingly to improve token-level adaptive training. This method assigns larger training weights to tokens with higher BMI, so that easy tokens are updated with coarse granularity while difficult tokens are updated with fine granularity. Experimental results on WMT14 English-to-German and WMT19 Chinese-to-English demonstrate the superiority of our approach compared with the Transformer baseline and previous token-level adaptive training approaches. Further analyses confirm that our method can improve the lexical diversity.