If one parent is AMHA and the other is AMHR, the foal is not eligible for either registry. In order to get AMHR papers on your foal you will have to get the AMHA parent registered AMHR.
It will cost you $400 plus $60 (assuming the stallion is 3 years or older) to get the sire registered AMHR. Once he has his AMHR papers, you send in a late stallion report ($25) and then you can get the foal registered.
If the mare qualifies for AMHA (5+ years old and 34" or under) you can hardship her into AMHA and then you will be able to get AMHA papers on your foal.