Do I misunderstand you or do you suggest that the customer object should include the list of all invoices? That does not scale. Imagine if it is something more common like transactions where a user can have made thousands or tens of thousands.
It can contain a link to the list of all invoices. So you could have /customer/<cid>/invoice which lists all invoices for the customer which are actually just links of the form /customer/<cid>/invoice/<iid>