Should one disclose his/her family information in an academic job interview?
It's probably best not to bring up family information at all during an interview. The committee wants to focus on your professional qualifications. They've probably been given strict instructions from HR not to take into account things like the applicant's sex or age, which are not professional qualifications. Different people may have different expectations about how formal a job interview should be, but in general it's not a casual get-together where we get to know each other.

Often a committee will want to understand why you are leaving your current position. Basically they want to make sure you didn't leave your current position because you did a bad job there and got fired. This becomes particularly relevant if the job you're applying for is at a professional level less than or equal to the level of the job you're leaving. In this context, it may be OK to mention your family if they're the reason you wanted to change jobs. E.g., you needed to move from Indiana back home to California in order to care for your father, who is old and unable to live independently anymore.

Another common situation would be the "two-body problem," where you and your partner are trying to find jobs in the same city. I would not bring this up at the interview stage. It's not relevant at that stage, because they haven't even offered you the job yet.

If you have young children, I wouldn't mention that at all. Many people in academia have very old-fashioned expectations about the academic lifestyle, e.g., that a high-powered academic must not be distracted by child-rearing, or must have a "faculty wife."