I think this is the idea. It includes blended families, fatherless families, etc.

Examples:

https://books.google.com/books?isbn=1441233504
Robert J. Keeley - 2008 - ‎Religion
All of this formed an overarching layer to the **actual nuclear family that existed at the time. The nuclear family was different than it is now**. Today a family generally ...

https://books.google.com/books?isbn=0822316870
Jane Feuer - 1995 - ‎Performing Arts
And although the dream is tainted — in both cases the tribe couldn't gather without the actual nuclear family at its center — it gives us an alternative to the ...

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Note added at 40 mins (2015-06-08 05:57:57 GMT)
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https://books.google.com/books?isbn=0292783140
Jack Boozer - 2010 - ‎Performing Arts
... as the working woman's portrayal remains largely contentious, and **as the nuclear family ideal, if not the actual nuclear family**, continues to reign supreme.

community.babycenter.com/.../from_the_feminist_vault_sit_down_for_this...
Oct 31, 2012 - However, **I don't think the actual nuclear family structure is or was automatically patriarchal** in nature because patriarchy, in the truest sense of ...

Alternatives: family members with whom the subject lives.
(I would be reluctant to use "nuclear family" because the definition of the latter does not require cohabitation.)
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Nuclear Family | Definition of nuclear family by Merriam ...
www.merriam-webster.com/dictionary/nuclear fam...
Merriam‑Webster
Medical Definition of NUCLEAR FAMILY. : a family group that consists only of father, mother, and children—see extended family.

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Note added at 1 hr (2015-06-08 06:55:07 GMT)
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(Also, for purposes of medicine and psychology, the relevant people are the people in the household -- indeed whether they are family members or not.)

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Note added at 1 hr (2015-06-08 06:59:33 GMT)
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2nd reference:
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Extended family - Wikipedia, the free encyclopedia
en.wikipedia.org/wiki/Extended_family
Wikipedia
The family changes from immediate household to extended household. ... it can be helpful for extended family members to share a single household in order to ..