Hi Ellen, you will have to forgive my ignorance on this, but could i ask what is on your partners birth certificate, male or female, because from what i can gather it has to be ether male or female they don't issue certificates for hermaphrodite or intersex, at least not here in England, i could be wrong, is that the "True hermaphrodite" bit?
Any way i would think your getting married would depend on what is on your partners certificate, if they allow homosexuals to marry in NY then you have all bases covered as i think you yanks say.:D
If she is down as a girl you can marry as a homosexual couple, if shes down as a man you could marry as a straight couple.
If hermaphrodite's are recognised on birth certificates in the U.S well..? that's a tough one.
Good luck my friend.