Background: Family carers, as a "shadow workforce", are foundational to the day-to-day integration of health service delivery for older family members living with complex health needs. This paper utilises Haggerty's model of continuity of care to explore the contribution of family carers' to the provision of care and support for an older family member's chronic condition within the context of health service delivery. Methods: We analysed data from interviews of 13 family carers in a case study of primary health care in New Zealand -- a Maori Provider Organisation -- to determine the alignment of family caregiving with the three levels of continuity of care (relational continuity, informational continuity, and management continuity). Results: We found alignment of family caregiving tasks, responsibilities, and relationships with the three levels of continuity of care. Family carers 1) partnered with providers to extend chronic care to the home; 2) transferred and contributed information from one provider/service to another; 3) supported consistent and flexible management of care. Discussion: The Maori Provider Organisation supported family carer-provider partnership enabled by shared Maori cultural values and social mandate of building family-centred wellbeing. Relational continuity was the most important level of continuity of care; it sets precedence for family carers and providers to establish the other levels -- informational and management -- continuity of care for their family member cared for. Family carers need to be considered as active partners working alongside responsive primary health care providers and organisation in the implementation of chronic care.