For a missionary, learning the language is extremely important. Knowing the language of the people is the key to communicating the gospel, being accepted into the culture and being able to feel “at home” where ever it is you live. Therefore, it is not only important for “the missionary” to learn the language but it is also important for his family (including his wife and children) to learn the language, so they also can carry out the above goals.
Living in a new environment demands that the language of that environment is learned to be successful and without limitations. For our children, learning the language is of the utmost importance.
One article says it this way:
“A bilingual environment is most often a necessity, not a choice.
Many discussions of the advantages or disadvantages of early bilingualism seem to be based on the idea that a bilingual environment is something that parents choose for their children. This, however, is usually not the case; young children growing up bilingually are for the most part doing so because there is no way that they can grow up monolingually. For example, it may be the case that the child interacts regularly with monolingual individuals, some of whom speak one language (e.g., teachers and classmates who speak only Italian), others of whom speak another (e.g., parents who speak only French). Other children may grow up in a community where most people speak the same two languages on a day-to-day basis. The usage rules for these languages determine when a particular language is spoken. Imposing changes in these conventions so that all bilingual speakers in the child’s social world would limit themselves to one and the same language in all circumstances is not only impossible but also ethically dubious, because it would infringe on individuals’ linguistic rights.” 
Our children are still young, and so I don’t have much experience in this area, though I have observed how our children have adjusted so far and have done some research to help make sure we are moving in the right direction.
I think there are different approaches to how you implement the languages based on how hard a language is and the age of the child learning the “new” language. But it is clear, as stated from above that missionary kids should learn both languages if the language of the people among whom they live is different from the native language of the parents.