I thought you couldn’t get legally married in Japan. Or do they mean a metaphor of cohabitation?
You can in Sibuya, Kodama Naoko made a manga talking about it. However it seems to be a little different of heterosexual ones.
Also, this is a serie of anthologies, this is the first, then they have another like which flowers or something like that and in july they'll released another a little ecchi. Horay!