This paper proposes an adversarial training method for the multi-task and multi-lingual joint modeling needed for utterance intent classification. In joint modeling, common knowledge can be efficiently utilized among multiple tasks or multiple languages. This is achieved by introducing both language-specific networks shared among different tasks and task-specific networks shared among different languages. However, the shared networks are often specialized in majority tasks or languages, so performance degradation must be expected for some minor data sets. In order to improve the invariance of shared networks, the proposed method introduces both language-specific task adversarial networks and task-specific language adversarial networks; both are leveraged for purging the task or language dependencies of the shared networks. The effectiveness of the adversarial training proposal is demonstrated using Japanese and English data sets for three different utterance intent classification tasks.