Is a husband's apostasy realized merely by his repeating a statement made by someone who was reviling religion, a statement that was about him? And what is the correct course of action for the wife in this situation?

What your husband did is not disbelief, because he did not curse the religion; rather, he narrated the saying of someone who did. Narrating disbelief is not disbelief. Therefore, you are not required to tell him what happened, nor to ask him to repent. You must avoid obsessive thoughts (waswas) and turn away from them, paying no attention to any of them, for indulging in such thoughts leads to great evil.