There is no such thing as a ‘typical’ Roman house any more than there is a typical modern house. There are, however, some common key features and rooms.
The atrium, was a large central hall which was the centre of household life. Guests would be greeted here, the household gods might be worshipped at their shrine, and women might direct the household slaves in their duties. In the centre was a square roof opening through which rainwater would fall. Directly below this was the impluvium, basically a basin for collecting water which was connected to an underground cistern. These were often inlaid with marble and surrounded by mosaics.
Usually surrounding the atrium were the family’s main rooms; the bedrooms (cubicula), the dining room (triclinium), a study (tablinum), and the kitchen (culina). Houses might also have internal courtyard gardens and in Pompeii they often have at least one upper floor.
A wealthy Roman citizen might live in a large house separated into two parts, one facing onto the street and one accessed via a passageway or through the tablinum. This provided increased security. The Romans did not have the same concept of defined ‘public’ and ‘private’ spaces as we do in the modern world; any room in the Roman house might be opened up to a guest at a moment’s notice.