If I were to apply for Interactive Design positions, I would certainly include a portfolio. However, coming from a background of Web Design, I don't necessarily have the best ideas on how to distinguish myself as an interactive designer. What must I put into my portfolio, or how must I organize it, in order to make it clear that I know how to be an Interactive Designer?
Might just be me but if I was hiring I'd be interested in seeing how you got to your solutions, not just the solutions themselves. I'd want to see how you think, why you did certain things and a broad base of materials that illustrate your skills across IxD -- be it wireframes, personas, mental models, sketching, facilitation, etc.
Anyone can learn tools (e.g. OmniGraffle, Visio, InDesign, etc.) but you can stand out by showing how you apply your skills to solving problems.
I'd suggest giving Whitney Hess' article a read, I think it address well what people are looking for in IxD portfolios:
Show off your enthusiasm for this type of work. List groups and communities you participate in, posts you've written, links to proof-of-concepts you've done on your own, scan in "your napkins" and put them up if they show off your thought processes, link to answers you've supplied on listServes,.. and so forth.
In addition to Benry's answer, you could perform some usability testing to demonstrate understanding of evaluation as well as design - perhaps a heuristic evaluation either of your own work (different versions, showing improved IxD) or an existing interaction that you love/hate.
Ultimately your portfolio is going to influence your potential employers by showing them your skills, approach, personal style, software adept with etc. Having a good range of design and evaluation pieces in your folio should help to suitably impress.
Benry put it nicely. Assuming your site has more than one page, then it had navigation. Navigation is an interactive element. Is there a form on the page? Any JS you used? People interact with websites. Think from that perspective.
I spent a year at Intuit just helping them with static websites. My title was interaction designer.
There is only one place you have not looked. And it is there...only there, that you will find the master. - The Last Dragon