Hinae Hibajiri is the mother of the protagonist Hidomi Hibajiri in FLCL Progressive. As the owner of a small establishment called Cafe Hibari, she serves as a central figure in her daughter's home life. In sharp contrast to her daughter's quiet and withdrawn demeanor, Hinae is portrayed as being very outgoing, excitable, and cheerful. Her personality is notably bubbly and expressive, a trait she maintains even when dealing with serious or frustrating situations, such as when she brandishes a knife in an attempt to get a simple "good morning" greeting from her sullen daughter. She directly comments on Hidomi's behavior, describing her daughter's personality as a "tsundere persona" that is becoming more polished every day.

A significant aspect of Hinae's character is her role as a single mother waiting for her husband to return home. She and Hidomi share this experience of his absence, but their approaches differ. While Hinae is growing tired of waiting and considers closing the cafe to move on with their lives, it is revealed that she had kept the business open largely in anticipation of his eventual return. This emotional burden lies beneath her typically sunny exterior. In one instance, she expresses to Hidomi that perhaps it is time to stop waiting for him, showing a more serious and weary side that contrasts with her usual cheerfulness.

Hinae demonstrates a notably forgiving and non-judgmental nature, particularly in her interactions with the enigmatic Julia Jinyu. After Jinyu deliberately runs over Hidomi with a car, Hinae does not hold a grudge. Instead, she gives Jinyu a job as a maid at Cafe Hibari the very next day as a way to make amends for the accident. Even when Jinyu struggles with simple tasks and breaks dishes while learning, Hinae remains patient, emphasizing a positive customer experience and not faulting her new employee for the mess. This act of quickly hiring the person who harmed her child demonstrates a unique and impulsive sense of logic, characteristic of the series' tone.

Hinae's relationship with her daughter is the primary driver of her role in the story. She cares deeply for Hidomi and is shown trying to connect with her, even teasing her about her crush on a boy named Ko Ide. Their dynamic is strained by Hidomi's emotional isolation, but they eventually reconcile and make the decision to run the cafe for themselves, strengthening their bond. Her own emotional arc ties directly into the series’ central theme of letting go and moving on from the past, as she ultimately must decide to stop passively waiting for her absent husband and actively participate in her own life and the life of her daughter.