firewalled delegation problem

[Vargas Miguel]

I have a split DNS implementation because we have private internal 10.x.x.x
addresses.  We have delegated several sub-domains from our internal domain.
So let's say I have three zones, acme.com, a.acme.com and b.acme.com.  If a
nameserver for a.acme.com gets a query for host.b.acme.com it doesn't work.
I think the problem is that the name server for a.acme.com tries to go to
the internet root servers to find acme.com but my internal acme.com is not
reachable from the internet.  

Should I make all the name servers for the sub-domains slaves of the
acme.com parent domain?  What about NS entries for the parent domain in the
sub domains, would that work?

TIA