Yes, Jodi's family believe that he is guilty, although they did not think that way in the beginning. Jodi's mum went to visit Luke two days after Jodi was murdered to comfort him, and many of her family members told police Luke was a "nice lad" in their earliest statements.
It seems, however, they were told many lies, and led, by police investigators, to believe that the police had a rock solid case against Luke (when, right from the beginning, they had nothing). For example, Jodi's brother told me repeatedly that there were "strands of Luke's DNA all of her body." I told him it wasn't true, I told him I had the DNA results right there in my house and I could show him - he called me a liar and repeated his claims about the DNA. I offered to meet Jodi's mum and show here everything I had uncovered - initially, she agreed, but then cancelled.
When Corinne received information about a credible suspect very early in the case, she called Judith to alert her. The call went to the answering machine. Judith called the police, who came and set up recording equipment on her phone, not to capture Corinne's information about this person, but to try to gather evidence against her and Luke. It's no wonder Jodi's family are so convinced - they were fed a relentless diet of assurance by police, who were simply not in a position to be giving them such assurances.