The map on that Assyrian site showed an indistinct area that seems to include some of the same upper mesopotamia, up into Turkey and over into Iran...
But I'm gathering that they're distinct from each other and that Kurds tended more to the east, while Assyrians were more to the west in that general region? Assyria centered on Nineveh, and Kurdistan from Mosul or so, eastward?
http://www.khazaria.com/genetics/abstracts.html
Jewish Genetics: Abstracts and Summaries
...At the present time, it is known that Eastern European Jews have a significant Eastern Mediterranean element which manifests itself in a close relationship with Kurdish, Armenian, Palestinian Arab, Lebanese, Syrian, and Anatolian Turkish peoples. This is why the Y-DNA haplogroups J and E, which are typical of the Middle East, are so common among them...
Assyrians held much of the territory on that map at one point, cuz they had a huge empire.
http://www.keyway.ca/htm2002/ancassy.htm
This page has a lot more maps, cuz different times had different "borders" for the territory they held.
http://aina.org/maps/historic/historic.htm