This will end in flames. Alignment discussions always do.
Harry himself is Chaotic Good. He is a strong proponent of "doing the right thing." He also frequently expresses the belief that rules and society get in the way of doing the right thing, more than they help. On more than one occasion, he has not only ignored the rules, but gone out of his way to thumb his nose at the establishment.
Murphy is Lawful Good, though heavier on the Lawful side. She truly believes that the law is there to help people, and that doing things by the book is the right way. She's also a strong proponent of the needs and rights of the "greater good," focused more on society as a whole than any given individual. However, she has frequently bent the law in order to do "the right thing," which pushes her out of the Lawful Neutral alignment.
Marcone is Lawful Evil. He has no compunction about using any means necessary to achieve his ends. However, of paramount concern to him is order (with himself at the top). He rules both himself and his organization with an iron fist.
Bianca is Neutral Evil. She is, ultimately, incredibly selfish. While she is able to run her own organization, and to play at least moderately well in the Great Game of the vampire courts, she has shown a remarkable lack of discipline on a personal level. Or maybe Harry just brings out that side of her....
Bob is Chaotic Neutral, or at least Neutral with Chaotic tendencies. While he is also selfish, he is not interested in pursuing his interests at the expense of others. He is a lone wolf, who is not at all interested in working with any larger organizations. He also frequently encourages Harry to take the most expedient solution, even if some people might get hurt along the way.
Billy is Neutral Good (although he would probably self-identify as Lawful Good). He is entirely about "doing the right thing." He falls into the Neutral category because of his views on authority and group dynamics. He wants to be part of, and to lead, a pack. And, he wants cooperation with the other supernatural critters. But, he very deliberately chose to be a vigilante, to work outside the established system.