As to your specific layout I'd stick to tables if you need to have side by side content. Just create an HTML table with a single row and two columns as a wrapper around your panels and you'll be all set.

I'm glad you suggested that as well - now I don't feel so stupid! ;)

I always use tables for something like that, and it always works fine. I've had some web designers "scoff" when I tell them I use tables when I want to put things side by side.