The mediation request could be a genuine attempt to have constructive discussions about contact, or it could be that the parent requesting mediation is intending on making an application to court re the child arrangements and therefore is required to attend a MIAM before submitting the application.
if you are the other parent, you could agree to attend a joint session and provide the mediator with the relevant information as to why the other parent is having supervised contact only. At least then you can say you did try mediation rather than just refuse point blank.
Supervised contact is not usually long term except for extreme circumstances and where there are safeguarding issues for the children. Obviously I don't know any details, but perhaps there may be room in the future for the children to have time with dad/mum in a contact centre where they can monitored by staff so the children are safe but they have a more relaxed contact time with him/her than they would do with a third party watching over the contact.