The male could definitely be a combination pied, but it's hard to say without pictures from the front. Since none of the babies look like combination pieds (it would be easier to tell with more pictures), the father is probably not
double factor dominant pied, just single factor and recessive pied. If the male was double factor dominant pied, all
of the chicks would be single factor dominant pied, and none of them seem
to be, but pictures of their fronts might reveal otherwise. I can't quite tell if your male is opaline since I'm not very good at spotting it/identifying it, but if he is then all the female chicks would also be opaline and all the males would be split for it.
Lutino masks other mutations, especially recessive ones, so she is probably split for white base and recessive pied, in fact she could even be
recessive pied. Since all of the babies appear to be recessive pied, and the chance of getting even one recessive pied baby is 25% if the mother is split for it, chances are your female is recessive pied but it's simply masked by the lutino gene. When two ino genes are present in a budgie, the only mutations it does not mask are cinnamon (creating the lacewing variety) and yellowface (creating the creamino variety in albinos). All the chicks will be split for ino (lutino or albino).
The only other thing the mother could possibly be is a dark-eyed clear, which is all yellow or all white and it's a mix of recessive pied and clearflight pied. But they have dark plum coloured eyes. So your female is probably just a lutino masking recessive pied.
I hope I helped. Those babies are just adorable!!