In this context, there seems two conflicting (i.e., cannot be simultaneously satisfied) duties: to be honest (to the Nazi officer) and to save others' (the Jewish family's) life.
A Kantian, may argue that if a duty is moral, it means that it should be conceded by all the rational people, since it is a priori and universal. Therefore if it is moral to tell the truth to Nazi officers. Then, it means that to put other people on a dangerous situation is universally acceptable, which is absurd. Hence, we can see that the unconditioned principle "to be honest" may not be a moral duty in Kant's theory.
Actually, in practical, when we answering question, even we're trying to be honest, we cannot guarantee that all we spoke are 100% truth since we always make mistakes due to the lack of information and prejudice. Therefore, to be honest itself is a questionable duty, since nobody can always do that in practice. And in the Nazi officer's context, a practical answer could be " I didn't see any Jew." which can save the Jewish family's life and simultaneously can be justified to be honest somehow. Since I do not check if the Jewish family are actually Jew, therefore, it is reasonable for me to doubt if they are Jewish and it is honest for me to say that I didn't see any Jew. And similar procedures can be applied to many other dilemmas.