I did a little research for you. Unfortunately it is very hard to find a flat in Berlin. I experienced that firsthand last year. But there are some Initiatives and Organisations which can help you to find a flat.
1. The best would be if you go to the "Evangelisches Jugend- und Fürsorgewerk" (EJF) in Turmstraße 2, House 'K'. You can either call them: (030) 30 873-652 or visit the office on Monday, Wednesday or Friday. Which languages do you speak by the way? E. g. Monday and Wednesday you can get consulting in arabic as well.
2. You can register yourself and the other person on http://www.home4refugees.org/
which is still under development or on http://www.fluechtlinge-willkommen.de/
. Just klick 'You are a Refugee?' and you can register yourself. Flüchtlinge Willkommen (Refugees Welcome in english) connects refugees with apartment-sharing communities.
I hope that will help! Good luck for you two!