I'm assuming that you're looking for a professional website, not something that a nontechnical person could easily slap together on a site like Weebly.
If that is indeed the case, then I think the main problem that you are going to encounter is just the lack of real-world experience when hiring interns.
Most interns need mentoring. The goal of an internship is to work hands-on with other professionals in the same field so that those same professionals can share knowledge with those interns to help them prepare for a real-world job.
Even fresh-out-of-college workers need guidance and mentorship by senior developers.
It sounds like your organization is not one that works in the field of technology at all. Therefore, it seems very unlikely to me that there would be anyone around to guide the interns, should there be a problem. In fact, it's also quite unlikely that the individuals in your organization know how to run a software project.
If you do want to include some interns to work on such a project, you're going to need to hire, at a minimum, at least one really experienced Web developer with a track record of successfully delivering and successfully leading a team.
Building a real, professional website involves lots of skill and knowledge of several different components.
Additionally, there is also more to building a website than just development. You'll need people with skills in the following areas:
- Website design
- Image cutting
- Content Writing
- Knowledge of what makes a website faster. (Google Pagespeed, Webmaster Tools)
- Marketing experience
Of course, if you're okay with using a cookie cutter Web template on http://weebly.com or any other number of low-cost websites, then that is something that anyone should be able to do, including interns.
Just to help you understand what I'm basing this answer on, my experience on this topic is based on working in the industry as a project manager and as a Web developer, working with both US-based and India-based software engineers, developers, marketers, and designers. Not only have I mentored new developers first-hand, but I've also experienced being new and learning from more experienced people myself. Had I started freelancing after college -- or working a job with no other engineers -- instead of joining a company, I would not be at the same experience level that I am today.