The first thing we learn about Marji's mom is that she's pretty revolutionary: "Her photo was published in all the European newsletters" (1.15) after a political protest. Marjane is proud of her mother, but her mother is scared. In a country where women are pressured to all be the same, having an identity is dangerous. Marji's mom has the same conflict about her daughter: She wants her to live her own life, emphasis on the word live. You have to be alive to live the way you want to be.
In order to stay alive, Marji's mom has to be resourceful. She's super clever, thinking up the idea to smuggle rock posters for Marji into Iran in the lining of her dad's coat. Marji eventually realizes that "For an Iranian mother, my mom was very permissive" (17.41). This almost gets Marji in trouble when she wears her punk-rock clothes in public (a more conservative mother would certainly have forbidden her daughter from doing so), but Marji takes after her mother in one major aspect: She's super resourceful on her feet, and so she's able to talk her way out of it.
There's one more thing Marji's mom is good at, and that's lying. (That's probably why she's such a good lie detector herself.) She's not lying in a bad way, though. She's an expert at changing the subject away from something terrible, like the death of their neighbors (it's sad that this is something that even has to be done), but she's also really good at making Marjane think that she's a good cook, even though Marjane is a terrible cook.
Marji thinks her mother is very strict. Mom is a great lie detector, and always seems to know when Marji isn't telling her the truth. Marji calls her mother a "dictator" (15.24), equating her with some of the biggest villains in the war, but only because she doesn't understand that her mother isn't restricting her freedoms for the fun of it. Honestly, she's doing it to keep her daughter alive. Iran is a dangerous place, so we think Marji's mom is allowed to be a little over-protective.
In fact, for living in a constant war zone, she allows her daughter a ton of freedom to make her own mistakes… and learn from them. If Marji was sequestered away from the rest of the world, like many young women in Iran were at the time, she wouldn't have grown up to be the woman that wrote this book. Let's pause here for a moment of gratitude for Marji's mom.