The houses of the rich may well have had a physical distinction between these spaces, but physically dividing one’s house that way was a little more difficult for anyone else. Greek houses, as shown primarily by evidence from Olynthos and Athens,* tended to be organized around a courtyard and sometimes a colonnaded pastas. Some houses had an upstairs. Some did not.
[Ancient Olynthos Chalkidki, image by Christaras A]
[Source: Wikimedia Commons]
[Ground Plan, Source: Traveling to Nikiti]
*[Skip this if you’re not interested in sources] Olynthos is problematic in that it is not very close to Athens and provides evidence from a little later than the height of what most people call Classical Greece. However, it is also one of the best we have. The city was sacked and most of it was never reoccupied. The site gives us not only exact layouts for individual houses, but also evidence for what sorts of items might have been used in various rooms. The problem with studying Athenian houses is mostly a question of access. There is a lack of funding and most ancient houses are buried under buildings whose owners really don’t want you digging at their foundations thank-you-kindly. Then there’s the archaeologist who got into a spat with the Greek state and refused to release his findings. So yeah, evidence is kind of a big problem.
Antonaccio, Carla M. "Architecture and Behavior: Building Gender into Greek Houses." The Classical World 93.5 (2000): 517-533.
Nevett, L. C. "Gender Relations in the Classical Greek Household: The Archaeological Evidence." The Annual of the British School at Athens 90 (1995): 363-381.