Humans and other vertebrates have both specific and nonspecific immunity while invertebrates have only

The answer is nonspecific immunity.

Nonspecific immunity includes the first and the second line of defense against pathogens. This involves skin and fever. The specific immunity includes not only the first and the second line of defense but also a third line. This third line of defense involves antigens, macrophages, t-cells, etc, and the aim is for an organism to gain immunity for a disease. The third line of defense and everything it involves is not characteristic for invertebrates, thus, they have only nonspecific immunity.