this problem is caused by the fact that IE likes <object> tags and Firefox likes <embed> tags. To make a media player that will be displayed in both browsers you need to use both kinds of tags.
It is common to arrange the tags as follows:
<object> ... settings for IE ... <embed> ... settings for Firefox ... </embed></object>
Notice that the <embed> block is completely enclosed by the <object> block.
Generating these kind of tags by hand is tedious and error-prone, so I usually copy and paste some that work and then change just the url of the media file.
The new HotPot module can easily insert many kinds of media players so when it is released (probably in April), it will make your working life much easier !
all the best