Hi Jeane,
Have your baby's birth certificate to be registered in the UK as well, let your hubby do it and maybe he can proceed of getting a british passport!...I got the same story, the only difference is our daughter was born in the UK, thus we got her birth registered at the Philippine Embassy in London then we just waited for it to come through to the NSO system, we then applied her the Philippine passport. Now she holds dual citizenship!
No need for a DNA test, for as long as you submit the birth certificate with the copy of your passports then should be ok!..My hubby went to the immigration office in London alone for our daughter's british passport, after a week we received it...