Here's the deal: Publisher, Word, etc. are very poor at creating websites.
Making websites (to look good cross-browser, anyway) is not an easy task. Microsoft, Apple, Google etc. pay people lots of money to get their sites looking good in all the popular browsers.
There are certain defined standards for website making. Internet Explorer follows them ok, but has a habit (as with many Microsoft products) for inventing their own standards when they want to. Firefox, Safari and Opera (other major browsers) follow the official standards very well.
Since Publisher is also a Microsoft product, they (understandably) make sure it looks good in Internet Explorer. But in doing so, they don't really stick strictly to the standards, so it looks a little off in Firefox, etc.
Frontpage (or WebExpression I think it's called now) offers better compatability with the standards. Dreamweaver even more so (though it's expensive). But the best way is to write the code that sits behind the website yourself. But it takes time to learn, which is why most people don't, or pay someone else.
So, either stick with what you have but understand the tools you're using are pretty poor for the job, or try Frontpage (WebExpression) and see if that improves the site.