You need significantly fancier kit to let you fail over to battery-only supply, as the house AC and the mains AC need to be exactly synchronised if ever they are connected together. I think our battery and inverter are "just another" circuit in the fusebox consumer unit, alongside the kitchen sockets and whatnot. A system that keeps going during a power cut would also need a chunky great off-switch relay on the mains side of the consumer unit, so that once the house has been separated from the mains there is no chance at all of the two coming back together until the appropriate gubbins has done its wizardry to bring them back in phase.
Or I suppose you could have two inverters, connecting mains->DC and DC->house, so you need never be synchronised at all.