Of Swords and Parasols

The Dirk & Steele series, in order, would be Tiger Eye, Shadow Touch, Red Heart of Jade, Eye of Heaven, and Soul Song. Plus there are supposed to be some short stories scattered about but I've never bothered to track any of 'em down. Each book is pretty much self-contained, though, with characters from other books making only small background appearances at most, so you can definitely read them totally out of order without getting lost. She generally seems to split the POV between the couple du jour, and since one half of the pairing is inevitably unaware of the existence of the various paranormal sorts, the agency, and so forth, the new reader gets brought up to speed on her world at much the same time as the characters do.