Family unit

[TurningAroundAndSaying]

Family unit. Family unit.
It is family.
You do not need the word unit.

I suppose it depends on what you mean by family?

To me, family unit would imply those living together as a independent group. A family would imply other relations/generations not necessarily living together. I wouldn't refer to my DH and DC as my family unit in general conversation though.

The word you need in that case is family. That's the word.
The word family covers it.
Saying 'family unit' is as bad as phrases like: 'I saw with my own eyes' or 'due to the fact'.

Family unit is a term of art in many social services and demographic contexts. It usually means a group of immediate family members living in the same dwelling. In those contexts, "family" can encompass a broader group that includes extended family members.

Seeline and Seneca are, as ever, correct.
The family unit is the members of a family who live together. Family has a much broader meaning.

My daughter is family.

She, her husband and her children are a "family unit".

My FIL is family.

He and his wife are a "family unit".

The terms "family" and "family unit" are not synonymous.