The name of the concept is indeed split DNS or DNS views (as BIND configures them using view statements [documentation]). However, this alone does not answer your question as you want to forward the query from the internal view to the external view if the record does not exist in the internal view. I believe this is not possible. (I also believe this exact question has been asks many times before on ServerFault so you should've done some better searching. But as I myself was not able to find similar questions quickly, I'll forgive you and answer the question here again).
Split DNS is not an exact match for the question you're asking as it assumes you're going to set up a single DNS server which will provide different answers depending on which client (source IP address) asks the question. You want two DNS servers with forwarding between them. So let's give that a shot.
Your internal DNS server will be the master for all internal records and all external records. Your external DNS server -- hosted in a DMZ -- will only be the master for the external records. To avoid having to enter the external on both DNS servers, you should put those in a separate file, rsync that file between both DNS servers, and $INCLUDE [documentation; search for "INCLUDE"] it in both zone files. The internal server will then look something like this:
/etc/bind/named.conf.local
zone "example.com" {
type master;
file "/etc/bind/db.example.com";
};
/etc/bind/db.example.com (on the internal DNS server)
example.com. SOA ns1.example.com. hostmaster.example.com. (
2017030300 ; serial
3600 ; refresh
1800 ; retry
604800 ; expire
600 ) ; ttl
NS ns1.example.com.
NS ns2.example.com.
ns1 A 192.168.0.53
ns2 A 192.168.0.153
$INCLUDE /etc/bind/db.example.com.external
internal1 A 192.168.0.5
internal2 A 192.168.0.12
client5 A 192.168.0.23
/etc/bind/db.example.com.external
This file needs to be synchronized manually or via cron between both DNS servers.
example.com. A 203.0.113.80
MX 10 mail.example.com.
mail A 203.0.113.25
www A 203.0.113.80
Some things to keep in mind are the SOA and NS records which need to be defined on both DNS servers and need to be specific for the internal or external zone. So everything above the $INCLUDE statement needs to be custom fit for each DNS server. Next both internal and external DNS servers include the external entries. Finally only the internal server specifies the internal records.
A small issue is that you cannot overwrite entries. So if you have a public entry (e.g. www.example.com pointing to 203.0.113.80) but you want to overwrite that for the internal DNS server to point to 192.168.0.80 that this needs to be done by not listing that entry in the shared file but specified separately underneath the $INCLUDE statement on both servers.
