I'm applying for a postdoc (Computer Science) and some positions ask for the contact information of 3 references. Beside my Ph.D. supervisor, I work with other departments in my institute, but mostly with the postdocs who were in charge of the projects. For instance, the professor head of department X knows who I am and that I did/do collaborations with them, but has no idea about the details. However, his postdoc researcher can provide much better detail regarding our collaborations and etc.
Nevertheless, I have a feeling that the employers (especially in academia) rely on professor-level references than a postdoc. So, I'm not sure about this situation.