the important question is: how could you marry officially without a passport? For marriage you had to produce a passport, a birth certificate and a certificate of not being married, at least. In what country did you marry and how long ago? What's happened to your passport? If it is not valid any more, why couldn't you renew it? These are question, which, I think, the BAMF, the Ausländerbehörde and every lawyer will ask you.
Your chance to get an asylum naturally depends on your reasons and your country of origin (or the country from which you came to Germany).
If your asylum is rejected, you can try to apply for a family reunion without leaving Germany but you will never get a residence permit without passport, or you must give a very strong proof, that obtaining a passport is not possible at all or the conditions for that can't be fulfilled for a very good reason. The Ausländerbehörden in Germany are very hard on this point. You can stay with so called Duldung (Toleration paper) for some time, but it is very unsafe.
For the hardship case it is mostly not enough to have a wife in Germany. These are mostly cases for people who live here for a long time, learn the language are well integrated, work etc. Or you must have a strong humanitarian reason. Or little children. But in each case you normally need a passport to have a residence permit of any kind (except for if you get a protection status).