Can I count unpaid internships as volunteer experience?

I wouldn't consider them as volunteering. Work experience and volunteering both hold their values. None is more impressive than the other I feel. For example, if you have volunteered to help a small town somewhere get new homes and a working water supply, that is not insignificant compared to someone working in a lab as a intern.

A quick and fast rule is volunteering is community service like at a food bank or some other insert item drive. Unpaid internships are generally work experience as it relates to professional skills like graphic design et cetera. The big grey area is in helping family members and volunteering with your place of worship notably with kids. At my place of worship I help out with classes for elementary schoolers and have the option of being paid or getting volunteer hours as some schools in my area require x volunteer hours/ semester. Though it tilts unpaid internship. As I said to the people it doesn't matter what you list it as long as the category is in the same ball park. On the college application what matters is the description of the activity. For example if your family owns a family company you can list that as volunteering or employment but if you list it as "I work for my family in their shop" or list it as " I am a supervisor at xyz store and I do xyz duties. I hope that makes sense.

Hope this helps and feel free to comment if you need clarification.

PS A tip is to quantify your activity discription.