Adding a border to an IFrame is no biggie - you do it like this e.g.:
border: 4px solid #000;
-moz-border-radius: 15px;
border-radius: 15px;
>
I know this is a rather old thread, but I found a valid work around for it that the others didn't cover.
What you're seeing is a z-indexing issue. All you need to do is put your iFrame into a DIV, and set the DIV's and iframe's position to absolute. Then set your z-index in CSS. It works great with Youtube videos in bubbles!