I fyou need to send a DNS search path to DHCP clients along with all the other details it seems you do it like this (in /etc/dhcpd.conf):

option domain-name "internal.usefulthings.org.uk usefulthings.org.uk";
option domain-name-servers 192.168.8.1, 192.168.8.2;

Took me a while to find that one!