They could, but it would have to be the same MobileMe account on all machines - you can't add data from one person's account to another person's account in the manner that they would like. Therefore, if they go the MobileMe route, they would need to get a generic "family name" account and be aware that all the information that one person adds will be available to the other.
However, you can publish your calendars to your MobileMe server and then have the other person subscribe to them, and you can also share your Address Book in a manner similar to sharing your iTunes or iPhoto library; I have no experience of using this, but I suspect it would work the same - if your Mac isn't on or awake, the other person wouldn't be able to view it - but I don't know for sure and I'm also not sure if you can add new people to the other person's database (I very much doubt it, though!).