Can I apply for permanent residency or other type visa to not to worry about leaving every 90 days?

My husband has diplomat status here in China and is working for an embassy, however, I am not from his same country and have an American passport, thus, his embassy is unable to process me a diplomat passport. His embassy has told me they can only process a diplomat passport for me if I renounce my American citizenship, which I do not want to do. Therefore, even though we are already living here in an apartment and our children have been attending school in Beijing, I have only been given 90 day tourist visas to remain here.