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mmike,
this a delicate issue. Using your passport or renewing it could be interpreted as if you no longer have the well founded fear of persecution. As a matter of fact, I remember I have read some regulations stating on that. This is why the Refugee Travel Document, a document issued in lieu of your passport, is what you have to get, before traveling abroad. Also, the Advance Parole should work provided you urgently need to travel.
In the I-131 form (RTD application), they ask if you have got or renewed your national passport, and if your answer is yes, you have to provide an explanation. But, on the other hand, this is somehow a kind of contradictory or questionable requirement, because once INS approve your I-485 they stamp your national passport.
So, to be in the safe side better not to use or renew your national passport while you are holding an asylee status.
Also, to use your passport requires for you to have a valid visa to be re-admitted in the US. What kind of visa is that going to be? student, visitor, H1, etc.
I am not a lawyer; therefore, take my comment as one coming from an individual that has learned about this stuff from own experience, other\'s experience and from what I have read and searched for a little while.