Another short one, I’ll quote an older post in a forum:
River is not “half human half time lord”, she’s “human plus time lord”. That’s why it’s possible. It’s like getting mixed vanilla and chocolate ice cream (the type in the photo) versus vanilla ice cream with chocolate sprinkles on top. Both options feature both flavours, but it’s mixed in the former and just added on the latter.
Donna had her DNA change. River has DNA from two human parents that was mutated by the radiation (or whatever) in the TARDIS.
Ice cream photo taken from Wikipedia.