You can be granted refugee status because UDI assumes that you risk persecution in your home country as well. A refugee status gives you the same rights as your family member. For example, you will be granted a refugee travel document.
You apply for refugee status and a refugee travel document at the same time. If your application is granted, you will be granted a residence permit on grounds of protection and a refugee travel document.
Here you will find more information about the requirements and how to apply for refugee status and travel documents as a family member of a refugee.