According to jiraya, he said that mentally minato divided kyuubi chakra into yin and yang chakra. To finish it this mystery what i think is that the yin chakra cannot return to kyuubi.
Yin and yang chakra is like the two sons of rikoudou sennin.
Yin chakra is like the outside power that takes form.
Yang chakra is like the inside power that doesnt have form = kyubii's chakra.
So certainly naruto does have both yin and yang but only half of the two. Like 25% each.
I think Yin and Yang are not enemy. You should not use the hatred and love concept here. Actually, Rikudo was able to create all thing because he had both of them through Juubi.
Why Kyuubi might have his Yin?
Take Juubi for example. He has his Yin and Yang, and he has his body (the mazou). Without any of the Yin and Yang, the mazou can still live and be use to create the zetsu. Thus, actually, Yin is the spiritual energy of a biju while Yang is his physical energy. Given that these two can be replenish with time and experience, I am incline to think Kyuubi already got his Yin back by feeding on Naruto and by also experiencing.