The Lands of Ice and Fire depicts a map of The Known World:
We can see that to the South of the known continents of Westeros and Essos, there are two more, Sothoryos and, to the far South-East, Ulthos.
Anyway, as far as I can tell, this is the most complete official map that we have at out disposal.
We don't really know about the exact location of the equator of this planet, and about the size, shape and precise location of the continents of Sothoryos and Ulthos, so we don't have any certainty about:
- the exact location of the two hemispheres;
- whether the two continents are entirely located in the southern emisphere;
- whether they span both hemispheres, and what we see in this map are just their northernmost parts;
- what lies not only to the South, but also to the West and to the East of this map (to the North, and not very far, presumably, there is the North Pole).
As KutuluMike said in his answer, we can try to guess something about the location of these landmasses by the climates, which is the basis of my previous assumption that the North part of Westeros is close to the pole1, and that the areas covered with jungles lie in the vicinity of the equator, but since we also know that the climate is also ruled by magic, these can only be speculations at most.
There is also the possibility that Sothoryos and Ulthos are not as extensive as Westeros and Ulthos, and that the Southern hemisphere, wherever it might start, could be mainly covered by oceans, leaving the landmasses primarily on the North, pretty much like our Earth2:
1. But in fiction, there can also be planets where poles are deserts and equators huge glaciated mountain chains...
2. Because of the projection used by this map, Antarctica seems to be larger than it is in reality.