The practice began as early as the 4th century in Eastern Christianity (Eastern and Southeastern Europe, Western Asia, the Middle East); John Cassian founded one, and Caesarius of Arles created one for his sister and women attached to his own. Columbanus brought the idea of the double (or dual) monastery to Britain, after which it became popular in Gaul and Anglo-Saxon England. Hilda of Whitby was going to attend Chelles, but was trained in. monasticism by Bishop Aidan of Lindisfarne and stayed in England and started Whitby Abbey.
The Second Council of Nicaea forbade double monasteries in Canon 20 "because this becomes a cause of scandal and a stumbling block for ordinary folk." Although they allowed existing dual monasteries to be "grandfathered," no new ones should be created, but
Monks and nuns should not live in one monastic building, because adultery takes advantage of such cohabitation. No monk should have the licence to speak in private with a nun, nor any nun with a monk. A monk should not sleep in a female monastery, nor should he eat alone with a nun. When the necessary nourishment is being carried from the male area for the nuns, the female superior, accompanied by one of the older nuns, should receive it outside the door. And if it should happen that a monk wishes to pay a visit to one of his female relatives, let him speak with her in the presence of the female superior, but briefly and rapidly, and let him leave her quickly.
After the 12th century, dual monasteries became popular briefly, although eventually most monasteries evolved into wholly separate communities. In Sweden, however, the idea of a double monastery experienced a revival in the 14th century, especially due to the Bridgettines. I'll tell you who they were next time.