No --- they are not legally your debts. The family member can be a creditor in your IVA, for your debt to them, and get a dividend like all the other creditors -- they will, however, get copies of all of your financial information as well. They will be responsible for paying off the cards in full themselves.
My opinions are merely that .. opinions based on experience. Always seek professional advice.
IVA Completed 23rd July 2013 .... C.C. 10th January 2014 http://foggy.blogs.iva.co.uk