Configuring Active Directory controller and guest with Internet access under VirtualBox

I'm setting up two VMs under VirtualBox – one acting as an Active Directory controller, and the other joined to the domain. Both are running Windows Server 2008.

I'm trying to get the network settings right so that both VMs can access the Internet (they need to obtain an IP address from the host's network), and so that Active Directory works as well.

Everything was going fine until I installed the AD role, then that server could no longer access the Internet. I left the IP address to obtain automatically and bypassed the warning that appears, so I was surprised this stopped working.

I've fiddled with different network adapter options in VirtualBox and read up about them but haven't had any success so far. (Networking isn't something I have a strong knowledge of.) Does anyone know what the steps are to get this working?

Update, more detail:

Here is a list of different network settings I've tried on the domain controller. For all of these the DNS server has been set to 127.0.0.1 followed by the DNS servers used by the host.

Using "VirtualBox Host-Only Ethernet Adapter":

• Set to "Obtain IP address automatically" and picks up an address in the 192.168.56.x range
• No Internet access and cannot ping other addresses on the host's network
• Didn't test client accessing the domain controller

Using "Bridged Adapter":

• Set to "Obtain IP address automatically" and picks up a Windows auto-configured IP address starting with 169
• No Internet access and cannot ping other addresses on the host's network
• Didn't test client accessing the domain controller

Using "NAT":

• Set to "Obtain IP address automatically" and picks up a network configuration very similar to the host
• Internet access works fine
• Client cannot access the domain controller

Both VMs can talk to each other using "Internal networking" however obviously this means no Internet access.