Some universities arrange special tours around the campus/departments/accommodation for parents/supporters. ie parents and prospective students arrive together then split off into separate groups for tours that cater for their own particular issues and questions. This means students can ask questions that they might be scared to in front of their parents and vice versa parents can ask questions that they wouldn't want to in front of their offspring.
And yes I am talking about applicant/post offer visits not ordinary open days.
On the other hand taking a parent into an interview would be just silly even if it were allowed.