The PCC said the complaints were made under clauses one (accuracy) and five (intrusion into grief or shock) of the Editors' Code of Practice.
"This is an approach we would take as a matter of course in relation to significant stories and when we receive complaints where there is an obvious first party to the material.
"I can confirm that we have now received a complaint from Mr Dye's family under clauses one and five of the editors' code."
The PCC, an independent body which deals with complaints about the editorial content of newspapers and their websites, said it was now seeking additional information from the family and would then take the complaint forward.
Mr Dye was a keen Cardiff City supporter and the club had also complained to the PCC about coverage of his death.
The PCC has confirmed it would investigate the club's complaint, which said certain newspapers had "acted insensitively".
If the complaints are upheld, the publications involved would be required to publish the text of the decision in full.
The PCC says many complaints are resolved through mediation so "it would not be appropriate to speculate about the outcome of the complaints at this stage".