ORIGINAL: rtrapasso
EDIT: This assumes, of course, that the face-hugger and exploder are two different organisms... it could be they are part of the same being, with the face-hugger part being sort of a "placental" attachment that is shed from the embryo once it is ready to leave the host... alas, they failed to provide DNA analysis of the different parts (assuming it actually has DNA). [;)]
RE-EDIT: How's THAT for geeky?? [:D]
Placental? How mammalocentric of you. [:'(] There's lots better examples than that clunky mammalian placenta out there to choose from.
More likely would be some sort of asexual autofertility (think bee workers) or other asexual reproductive cycle. Even if it were an example of binary fission or other asexual reproductive life cycle, the new form would be considered a different organism once it left the host. A completely different organism that was indistinguishable from its progenitor by genetic analysis.
Your DNA analysis would be unable to differentiate such a spawned lifeform from the placental attachment theory you espouse above-both would have identical DNA to the 'parent' or 'placenta' that you mention. Assuming, of course, it has DNA. [;)] For myself, I would venture that Alien has SNA (sulfuric nucleic acid).