Family asylum has both advantages and disadvantages: If accepted, your family will have the same status and rights as you. That means your family, e.g. will also be entitled to privileged family reunification ("priviligierten Familiennachzug"). This option can be useful, for instance, if you are an unaccompanied minor refugee who is permitted to bring their parents to Germany- but not their siblings. Once your parents have obtained family asylum, they can bring their other underage and single children (i.e. your siblings) to Germany. Another advantage is that your family can stay in Germany independently. So, for instance, even if you separate from your spouse, they will be able to keep their residence permit.
But family asylum can also have downsides: as soon as your family members are also recognised as entitled to asylum or refugees protection, they will no longer be able to travel to their home country. Furthermore, after applying for family asylum, your own recognition may be re-examined or - in the event of a considerable improvement in the situation in your country - even revoked.
If you are uncertain whether family asylum is right for you and your family, seek advice from a counselling centre or lawyer. You can find a counselling centre nearby on the Pro Asyl website. Plus, at www.rechtsberaterkonferenz.de you can find lawyers who specialise in the rights of refugees and asylum seekers.