Other possibilities are:
1. he is too scared to talk because he has been told to keep silent as there is some threat to people he cares about.
Hmm, maybe threats against his children?
2. he knows there is no compelling evidence (this would be especially true if he is not guilty) and knows that the prosecution cannot possibly bring a case against him as long as he says nothing.
I don't particularly believe one thing or another about DH and I try to keep an open mind about his guilt or involvement, but one thing I do know for sure is that this case is beyond peculiar, especially as it now seems everyone, defence and prosecution, are doing their best to delay.
My guess is that this is intentional because DH and Karlie were just the tiny tip of a very big iceberg and delays help with the info gathering.
Sad to say it, but I don't think the death of a mother and her child are the biggest concern of the investigating teams at the moment.