If it was an unpaid internship, you weren't employed...period. By law, unpaid interns are not employees because the work experience is for the primary benefit of the student, not the business. Most companies that pay student interns do so to avoid FLSA liability.
Perhaps list the experience under the volunteer/extracurricular section of your application? If you're trying to figure out how to list it on your resume, put it under the heading "Work Experience" (which can include both paid and upaid work) instead of using "Employment History".