Does verbally assenting with "yes" to the words of a Christian woman who said, "May our Lord protect our children," while she means Jesus, peace be upon him, constitute disbelief, and does the husband's statement that this situation does not constitute disbelief entail anything upon him?

You erred in your compliment to her, but neither your statement nor your husband's statement constitutes disbelief (kufr), because takfir (declaring someone a disbeliever) is not based on words that could be interpreted as disbelief or otherwise. One whose Islam is established does not lose it except with certainty, and a specific individual is not judged to be a disbeliever unless the conditions for takfir are met and its impediments are absent. It appears that she invoked a 'claimed lord' while you intended Allah Almighty. Scholars have said: If there are ninety-nine reasons to declare a Muslim a disbeliever, and one reason to keep him within Islam, then one should act upon the reason that keeps him within Islam. You should ignore these whisperings (waswas), seek refuge in Allah, and engage in remembrance (dhikr).