But the third battery would be replaced by a GTI. This way, when batteries are full you send power to your grid and pay less to your provider. And if main power fails, you still have a 12V grid to produce for your router / laptop / TV / Freezer (depending on sizing).
I am first planning to use this king of GTI, but may be a home made GTI could be made from:
http://www.timnolan.com/index.php?page=solar-grid-intertie-inverter
http://electronicdesign.com/Articles/Index.cfm?AD=1&ArticleID=21575&pg=1
Let's see...