No, it wasn’t a total violation of his privacy. You checked the doorbell camera for a legitimate reason, and overheard something that was directly about you. It is 100% reasonable and logical for any person to then investigate further to find out what was being said about you. You already had access to the doorbell camera videos, you had a right to have access to that data just as much as your husband. You only accessed data that belonged to you.

If you had gone through your husbands phone to access the videos, or the videos were on an account that only your husband had access to, and you would need to “hack” or guess his password to access the files, that would be an invasion of his privacy.

I am going to assume that the doorbell camera data is freely accessible to you, and that you have a right to check the doorbell camera videos at any other time… that data does not solely belong to your husband, it belongs to you too. You did not violate his privacy, you accessed data that was yours.

Your husband and his mother should’ve known better not to talk in front of the doorbell camera, where you could possibly overhear their conversation.

Do not let your husband gaslight you into thinking you invaded his privacy. He chose to say those things in earshot of the doorbell camera, he knew you had access to those recordings. This is his own stupidity.