Praise be to Allah, the Lord of the World; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
It is lawful for the man to talk to the woman and for the woman to talk to the man if there is necessity for that like calling to Islam or answering Fatwas about Islamic knowledge or the like. Actually the voice of the woman is not Awrah (something that she must conceal). Allah Says (interpretation of meaning): {… then be not soft in speech, lest he in whose heart is a disease (of hypocrisy, or evil desire for adultery, etc.) should be moved with desire, but speak in an honourable manner.} [33:32].
So, Allah warns against being lenient and soft in speech and not actual talking. Allah told the women to say that which is good.
As for the Hadith you referred to we do not know it. However, there is a sound Hadith where the Prophet warned any two people of talking secretly in the presence of a third one as that will make the third person sad.
We believe then that the fact that two people talk in a language that their third companion does not understand can be considered as similar to their talking secretly in his presence, and that doing so has the same effect which is to sadden the third person. So, it has the same rule.
On the other hand, trust your husband and do not let jealousy drive you to suspecting him of bad things especially that your husband - as you mentioned - does the Dawah work and teaches the Qur'an. So, try to help him pursue this noble mission and do not become an obstacle to him.
We ask Allah to guide you and your husband to the right path and to make your relationship a good and trusting one.
Allah knows best.