Angela is the biological baby daughter of Warren and Janine, forcibly taken from Janine. In the TV series, Janine named her baby Charlotte before she was taken from her and raised as the daughter of Naomi Putnam.
In the novel Edit
Janine is assigned to Commander Warren and his Wife, being known as Ofwarren. It is rumored that the real father of Janine's baby is not Commander Warren, but her doctor, due to Warren's infertility, and Warren's Wife secretly arranged this to get a child. Janine delivers a seemingly healthy baby girl, who is immediately given to the Wife and named Angela. Unfortunately, baby Angela turns out to be a "shredder" and does not live.
In the TV series Edit
Janine is assigned to Commander Warren Putnam as Handmaid and surrogate mother, where she gets impregnated and gives birth to a daughter, whom the Putnams name Angela, whilst Janine names her Charlotte. Due to an affair with her Commander, Janine believes he is in love with her. He promises her they would run away together and be a family, though this is considered a lie so he could persuade her to do sexual activities with him that his wife wouldn't do. Naomi Putnam, his Wife, is obviously inexperienced with children and is bitten by Janine at one point when she tries to take "her" child from Janine.
In the ninth episode, 'The Bridge', Janine suffers a psychological breakdown after she is taken away from Angela and the Putnams to be reassigned to Commander Daniel. She is later able to make her way back to the Putnams and abducts her baby daughter. She is found standing on the edge of a bridge over a river, holding her daughter and threatening to throw herself off. When Warren tries to dissuade her, she becomes infuriated and reveals his promises to her and the sexual things he made her do behind his wife's back. Offred is brought forward to try and talk her down. She seemingly manages to get through to Janine, who hands over her daughter to Offred, only to go ahead with her suicide attempt moments later, jumping into the frozen water. She survives, but is taken to hospital in a critical condition.
Serena takes Offred out for a walk where they run into Grace Scott and Naomi Putnam with baby Angela, who is already teething and thus a bit twitchy. Naomi thinks that teething is a way for God to "test" her. 
Angela later falls ill, but physicians are unable to figure out what is wrong with her and therefore treat her. In the hospital, Serena Joy asks Naomi if Janine, who is brought by Aunt Lydia, could see the baby, after June suggests it as a way to save an already unstable Janine after hearing the bad news about her daughter. Her husband does not mind, but Naomi is more than apprehensive about allowing their estranged handmaid to see Angela. June takes an emotional Janine to see the ailing baby in the ICU. A former famed neonatologist named Dr. Hodgson arrives as a Martha (signed on a temporary transfer against Waterford’s knowledge), and is briefed on Angela’s condition by Dr. Epstein, who was very happy to see Dr. Hodgson. She runs several tests on the baby, but is still unable to pinpoint exactly what is wrong with Angela.
Naomi and Warren recieve the bad news from Epstein as Janine helplessly watches. Serena is greatly upset at Dr. Hodgson, but the doctor explains that there is not much more she can do and suggests that Angela should be made to feel comfortable and warm. Upon June’s suggestion, Janine is able to hold her daughter, and even removes her mask and gloves in order to touch and kiss her baby. This proves to save Angela’s life, as Aunt Lydia wakes up in the ICU and finds Janine in her underclothes holding a cooing and happy baby, seemingly cured by her mother’s touch.