The three common culprits are tables, frames, and style sheets. The solution is to restrict your use of style sheets to those elements that both browsers get. The URL is made up of a path and a filename. In general, use relative addresses for all the files on your server and use absolute addresses to link to files on other servers. Finally, make sure you upload the file where you say it will be.
Frames are useless without targets.
The pure-HTML way to change more than one frame with just one link is to point to a special frameset that specifies two or more new source files. No JavaScript required. In other words, the W3C discourages the use of deprecated tags, but such tags remain a part of the official HTML standard. Frankly, I don't think that day will come any day soon. It is my humble opinion that style-related HTML tags will continue to be supported by all browsers for many years to come.