I found that setting the attribute wmodein the tag <embed>to be equal window( transparentbefore it was set to before) solves the problem. Why this causes problems with combobox (and only with the list, afaict), I have no idea, but I'm glad I solved this problem.
EDIT: I found a workaround in the code, so I can still use transparent wmode. Apparently, the problem is that Flash Player does not dispatch Event.RENDER events when it is transparent in wmode. The trick is sending this event manually at key moments. This is my decision:
private function renderStage(e:Event=null){
stage.dispatchEvent(new Event(Event.RENDER));
}
myComboBox.addEventListener(ListEvent.ITEM_CLICK, renderStage);
myComboBox.addEventListener(ListEvent.ITEM_DOUBLE_CLICK, renderStage);
myComboBox.addEventListener(ListEvent.ITEM_ROLL_OUT, renderStage);
myComboBox.addEventListener(ListEvent.ITEM_ROLL_OVER, renderStage);
myComboBox.addEventListener(Event.CHANGE, renderStage);
It works.