Thank you for reaching out to Wefugees and sorry for the wait!
In order to apply for a Wohnberechtigungsschein, "WBS", you will need to have the following: German nationality, citizenship of a EU member state, or a residence permit for (at least) one year if you are a foreigner.
Here is the full list of documents you need to hand in, provided by the Berlin Service website: https://service.berlin.de/dienstleistung/120671/
(It's in German, please use a translation tool)
If you two have German passports, this may not apply to you, otherwise you need to have a residence permit for your application. Of course, it also depends on the amount of money you have and whether or not you receive other financial support. You would need to fill out a few forms, hand in bank statements showing your income, or study certificates if you're a student, etc. The application is handed to the Housing Office "Wohnungsamt" of your municipality. It's usually part of the "Bürgeramt"/ citizen's office.
Here is a helpful list of important German documents to download in English by the KuB - a contact and support service for refugees and migrants: https://www.kub-berlin.org/formularprojekt/en/translated-forms/english-applications-and-appendices/
I hope this information helps. Please let us know if you need any further assistance.
All the best,