This sounds a lot like a guitar-driven Stereolab (or even more, like My Bloody Valentine) in some places, and incredibly unique in others. The female lead singer (the way the liner notes are written, it's hard to tell exactly what the participants' names are here) has a really wonderful and exquisite voice, sort of soft and mellow but not even slightly overpowered by her musical accompaniment.
Instead of coming off as noisy and borderline metallic, like most of this type of adrenaline-powered guitar rock usually ends up being, "Places You Call Home" maintains a pleasant, dreamy, spacey soft-pop quality throughout, no matter how loud you crank it up. It's so hard to pin this band down to any sort of real "genre"; every time I think I've got these guys figured out, they turn around and do something completely unexpected.