It's worth looking at some figures from Google Books here...
1 - predominantly OUR
our/my motherland 79,600 / 22,200
our/my fatherland 105,000 / 53,800
our/my homeland 160,000 / 88,500
2 - predominantly MY
our/my birthland 105 / 431
our/my native land 130,000 / 234,000
land of our/my birth 130,000 / 256,000
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...
defend the/our/my motherland 8,470 / 8,060 / 186
fight for the/our/my fatherland 48,500 / 1,320 / 237
the/our/my homeland security 1,780,000 / 122,000 / 600
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...
my parents' motherland 5
my parents' fatherland 4
my parents' homeland 1,150 <--- (this is therefore my suggested answeras per Mari-Lou's earlier comment)
my parents' birthland 2
my parents' native land 158
land of my parents' birth 78