The latest edition of Harbrace Essentials, by Cheryl Glenn and Loretta Gray, provides guidelines for four different methods of citing sources; Modern Language Association style; Chicago Manual of Style; American Psychological Association style; and Council of Science Editors style.
Most teachers would agree with the following statement:
There is no single, "right" way to cite a source; there are various ways required in different circumstances and by different teachers, and it is important to follow your teacher's precise directions. -- Robert C. Evans :-)
If you are writing your paper for an English class, the preferred choice is probably the Modern Language Association style. If you are writing your paper for a history class, the preferred choice is probably the Chicago Manual of Style. You may want to ask your teacher which of these two styles of documentation s/he prefers.
For examples of how to cite interviews using the MLA and CMS methods, see the links below.