If you're looking for manga similar to Double House, you might like these titles. All recommendations are made by Anime-Planet users like you!
Rio Sakaki was raised by an unsympathetic father and a stepmother whose dream of a normal, happy life drove her to harass the poor girl and have her institutionalized. As a result, Rio developed suicidal tendencies and an aloof, distant personality that drove all potential friends away. But things change for the girl when she meets the studious, yet just as troubled Sahoko one day, and in time, Rio's icy exterior begins to melt. Together, the two girls quickly become fast friends and try to carve out their own happiness in a world that has neglected them.
In both these manga, two women from less-than-ideal backgrounds meet each other by chance one day and become close friends. Both have some very mild shoujo-ai elements (Pieta moreso).
Pieta has more romance and drama, whereas in Double House this is replaced by musing over the role of gender in society.
Shuichi Nitori is an elementary school boy with a secret: he wishes he were a girl and likes wearing their clothes. With the right outfit and his cute, effeminate looks, he is often able to convince people that he is someone else - or even something else. Unfortunately, although his best friend and object of affection, Takatsuki, accepts him as he is, she does not return Shuichi’s feelings. Moreover, school is an unforgiving place and Shuichi walks a fine line between liberating his true self and being labeled a freak by all his peers...
Double House and Wandering Son are both low-key, character-focused manga about gender etc. Tone and such are pretty similar, and there's not many manga that cover this topic without comedy or "traps", so if you're interested in one's themes you may as well check out the other.