OK, now here we go.
I found out what was happening and it's a bit tricky.
When using the AJAX request above, I used data from a normal HTML-Form. In the form tag opening the HTML-form I hadn't provided an action- or method-attribute. It was just like
<form name="bla">
...
</form>
Now what happened? I pressed the submit button of the form. The jQuery-event got triggered. But at the same time, the normal form event also got triggered. As I had set no action or method, it automatically assumed
<form name="bla" method="get">
...
</form>
That's what finished me off because the GET-paramers of course appeared in the URL afterwards. :)
I now use .preventDefault() in the jquery script to avoid the normal form getting submitted any other way than via AJAX.