Hi, living partner is only available in sandbox mode. Right now, if you're playing the female character in sandbox mode, you can have Patrick as your living partner. Do task for him (just visit him at the city park after midnight) & there will be chance for him to ask for a date. Later, he might propose during the date. You'll engaged to him and you'll get married to him after the apocalypse is over (after March 2009).
Once you get engaged to him, you can visit his home & do many activities as if you're at your own home. However, we haven't yet implemented this visiting part on current update. Upcoming update next year should be able to address this issue. If you're playing male character, the living partner is Cecilia (theatre) but we haven't implemented dating part yet. This will also be addressed in upcoming update.