The main reference is a page giving guidelines for what sort of equipment is required for connecting a solar system to the grid for net metering.
Of course there will be some requirements for that, and most systems that use the grid for "storage" aren't setup to power the house when the grid is down. Thus the system that isn't capable of powering the house without the grid is off when the grid is off.
The question of whether one can operate a house with solar+battery when the grid is down is not really answered by the article.