My family is pretty cool. They're understanding and intelligent. I think Miko would get these impressions as well, and would have quite an interesting conversation with my dad about topics such as politics and morality, or he could wow her with how far modern medicine has advanced. She probably wouldn't like my mom too much, because she would see that my mom didn't really like her.
My parents initial thoughts about her might be that she is some sort of eccentric due to her hairstyle. They would definitely approve of Miko after talking with her, though. She's a saint and some kind of genius, after all.