I am looking for a word that refers to the country in which one's parents were born. Something similar to mother-tongue except for location instead of language?
It's worth looking at some figures from Google Books here...
The above results suggest to me that mother/father/homeland are primarily associated with identifying shared biological and cultural origins. When an individual simply wants to identify his personal background, he's likely to avoid terms which are primarily nationalistic/militaristic...
Quite apart from those connotations (which are presumably unwanted in OP's context), there's a literal/figurative clash in forms such as my father's motherland, my parent's fatherland, etc. Plus there's obviously no reason to mention your parents' origins at all unless they're different to yours. But if you have to, the general preference is quite clear...