zofamily
n.— «Happy crawling all you Zofamilies!!! DID YOU KNOW????: That “Zofamily”—Pronounced like “So Family,” is the term used for: “Any family that considers their pets an actual member of the family.”» —“Welcome Dog Lovers!” Breeders-Corner.com June 6, 2007. (source: Double-Tongued Dictionary)
Further reading
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It is incorrect to say ‘happy crawling’ is a characteristic of a zofamily. Please remove. Zofamily is a loving state of mind and heart. I found the term used in a veterinary paper defined like this, “A zofamily is the term used for any human family that considers its pets to be a part of the real family.” So that concurs with your definition.