Ib's parents are one of the minor characters in the game. Ib lives with both her mother and father.
Nothing is known about Ib's father. At the gallery, Ib's father asks her if she understands a painting he was looking at.
At some point it's revealed that when he first saw one of Guertena's works, he had a nightmare the following night.
Ib's mother has somewhat a bigger role in the game. In the beginning of the game, she tells Ib she is allowed to wander the gallery, only if she doesn't get herself into trouble.
Depending on the ending, Ib's "mother" will appear as Ib is about to jump into the portrait with Garry. Garry doesn't see Ib's "mother" but Ib's "mother" is able to see Garry. Ib's "mother" tells Ib that she's been looking for her everywhere and her father is waiting. Ib is in a difficult situation because her "mother" yells at her, asking if she wants to see her parents again, and that she shouldn't be following strangers.
If Ib decides to go with Garry, Ib will return to the gallery where her real mom is looking for her.
If Ib decides to go with her "mother", they will hold hands and slowly walk out of the screen, Garry is asking Ib where she is going since he can't see Ib's "mother". Garry returns to the normal gallery, having no memory of Ib, depending if you give him your handkerchief or not.