Father: 
His name is Tadashi Katou. A man who seems cold-hearted at first. He is very stern and doesn't show his emotions very well but he loves his daughter dearly. He believes in discipline but goes to far with it. After his first wife died he had to raise Juri by himself but wasn't very good at it. He is distraught after Juri was caught and loves her very much. He owns a bar- not a restaurant.
Mother:
Her name is unknown. Not much is known about her since she died when Juri was about Shiuchon's age. Her death traumatized Juri and left her father and Juri by themselves.
Stepmother:
Her name is Katou Shizue. She and Juri's father married after Juri's original mother died so Juri resented her. Her stepmom really is a sweet lady who is very soft and loves Juri a lot. She doesn't know how to connect with Juri and feels depressed because of it.
Her half-brother:
His name is Massahiko Katou The child of Juri's dad and stepmother. I've never really seen the two interact so I really don't know what goes on between them.
I really don't think Juri gets a long with her family very well. Her father is very withdrawn and stern and she is upset o her stepmom taking her real mom's place- and since there is no interaction between her brother and her I don't think they are close at all, since Digimon's creator (Toei I think) likes two elaborate on sibling relationships. Even though she never complains about them- the only person she mentions is her stepmother but that's more of regret then anything.
Thanks to BrokenHeartedRuki for the names.
