Language mismatch remains a major hindrance to the extensive deployment of speaker verification (SV) systems. Current language adaptation methods in SV mainly rely on linear projection in embedding space; i.e., adaptation is carried out after the speaker embeddings have been created, which underutilizes the powerful representation of deep neural networks. This article proposes a maximum mean discrepancy (MMD) based framework for adapting deep neural network (DNN) speaker embedding across languages, featuring multi-level domain loss, separate batch normalization, and consistency regularization. We refer to the framework as MSC. We show that (1) minimizing domain discrepancy at both frame- and utterance-levels performs significantly better than at utterance-level alone; (2) separating the source-domain data from the target-domain in batch normalization improves adaptation performance; and (3) data augmentation can be utilized in the unlabelled target-domain through consistency regularization. By combining these findings, we achieve an EER of 8.69% and 7.95% in NIST SRE 2016 and 2018, respectively, which are significantly better than the previously proposed DNN adaptation methods. Our framework also works well with backend adaptation. By combining the proposed framework with backend adaptation, we achieve an 11.8% improvement over the backend adaptation in SRE18. When applying our framework to a 121-layer Densenet, we achieved an EER of 7.81% and 7.02% in NIST SRE 2016 and 2018, respectively.