I had the same Problem with jHTMLarea 0.7.5.
This Problem exists in other WYSIWYG-Editors too.
For fixing this you must edit your jhtmlarea.js File.
Search for:
designMode=on
Then delete this term and insert
edit.body.contentEditable = true;
..at the end of the function.
Make sure, that you setting contentEditable AFTER the inital-document is written like this:
[..]
initEditor:function(options)
{
var edit=this.editor=this.iframe[0].contentWindow.document;
edit.open();
edit.write(this.textarea.val());
edit.close();
if(options.css)
{
var e=edit.createElement('link');
e.rel='stylesheet';
e.type='text/css';
e.href=options.css;
edit.getElementsByTagName('head')[0].appendChild(e);
[..]
edit.body.contentEditable = true;
[..]
It seems to be a solution that runs on Firefox too, so you not need to make a Browser-switch. Take a look that you setting "contentEditable" to an HTML-Element like "body" or "div" and not directly to the "document"-Object.