What is the ruling on a husband repeating the Noble Verse: "And such days We alternate them among the people" with melody and musical intonation, and does this fall under the category of disbelief?

What happened with your husband is not disbelief (kufr). Rather, it appears he was beautifying his voice with the recitation of the Qur’an, and he will be rewarded for that. Reciting the Qur’an with melodies is not disbelief. So, leave these whispers (waswas) and do not pay attention to these delusions, for they are from the plots of Satan.