The APHA allows horses crossed with AQHA and JC horses to be registered as APHA. Only one parent has to be registered as APHA if crossed with AQHA or JC.
I'm not sure what the APHA's policy on DNA typing for parentage is though, but you should be able to register your horse as APHA. My mare is registered APHA because her dam was APHA. Her sire was AQHA.