As pointed out in other posts, the meter is only there to measure power, whether it is power consumed from the mains or exported from the PV cell generation. The inverter is there to convert the DC power generated by the PV cells into AC power for use in the house and any extra exported. The inverter will detect when a mains power failure happens and will automatically shut down, so no AC power output.
This is NOT some electricity company conspiracy to gouge money or any other weird interpretation. It is there for the safety of the electricity workers! Imagine if there was a power failure and the PV cell power remained connected to the mains (known as "islanding"), what would happen if a worker touched the live mains? Even though this is extreme, it is potentially possible for that worker to receive an electric shock, which would vary depending on many factors, but it could be fatal!
Now, how would you feel if your solar panel generated power resulted in a death??
That being said, there is no technical reason or regulation why you cannot have a switch to isolate your house from the mains in the event of a power failure. It is not generally done because to have it work automatically you need a sensor detect the power failure to operate the switch which would isolate the mains, but maintain the PV cell supply to the house. Failure of this control could result in feeding into the mains, so it needs to be fail safe. An alternative would be to have a manual transfer switch which would do the same thing as the automatic switch, but you would need to go to the meter box to operate the switch yourself.
These are a few things needed for this to work:
1. You will need to have an inverter which has an oscillator NOT dependant on the mains for the correct frequency.
2. Is you mains supply single or multi-phase power. Most solar generation is single phase, so in a multiphase house the solar power would only provide power to the circuits on the phase it is connected to. The others phases would not have power (there are ways around this but it needs a really good electrician)
3. The power generated by the solar panels is dependant on how sunny it is and the angle of the sun. So the power generated will not necessarily be the rating of the PV cells, it will be less. So, you cannot work on the rating of your system to work out how much you an connect, if you try to connect too much load the inverter may shut down, losing all that benefit. What this means is that you will need to monitor your generation and your consumption so the system is not overladed. Things of particular concern would be anything with a motor they they will overlap and burn out (especially refrigerators) and freezers!
A battery system is a whole new situation, but there are 3-phase systems available capable of operating "off grid" i.e. not connected to the mains. This introduces problems of size (which determines how long the batteries will operate), which in turn introduces 'cost' - how much is it really worth paying for being able to maintain power during a blackout? When was your last blackout and how long did it last??