Inko is Izuku's mother and cares deeply for him, as she often played hero games with him as a child and believed he'd be good hero. When her son turned out to be Quirkless, she started apologizing to him as if it was her fault and doubted his dream. However, once he developed a Quirk and got into his dream school, she felt guilty about her former beliefs and even made a costume he drew herself. She brought up her past beliefs and apologized for not believing he could actually be a hero, she soon told him that she would support him all the way, to his happiness.
She later showed that she was worried about the consequences of her son's new Quirk after seeing the damage done to his body. Indeed, after the ordeal at the training camp, Inko was completely against him resuming his studies at U.A. due to their inability to protect her son. Only after All Might convinced her did she relent but made Izuku promise to not hurt himself any more to which he did.
Hisashi is her husband, but he has not been seen in either her or her son's life, as his whereabouts and status are unknown. All that is known about him is that he took a work post abroad and that his Quirk allows him to breathe fire.
Inko meets Toshinori Yagi for the first time when he goes to her apartment to talk to her about the dorm system. Despite being nervous about having the famous All Might at he home and despite knowing that he is her son's idol, Inko does not hesitate to be against All Might's request and criticize him. After the latest events, she wants to pull Izuku out of U.A. High School, because she does not trust that they can protect her son. She also knows that Izuku looks up to All Might so much that she is worried this will lead him down the same blood filled path.
All Might manages to convince her after assuring her that he will take raise Izuku to prevent him from walking down a blood-stained path to heroism, and promises to protect her son from all danger, even at the cost of his own life. Inko is shocked at All Might's resolve. She states that all she wants is Izuku to be happy and tells All Might that he should never trade his life away for someone else's sake. She asks All Might to promise to live properly and raise her son, to which he agrees.