Enabling 2nd network adapter on Ubuntu 12.04 server VM

I have a fresh, updated copy of Ubuntu 12.04 server. It's configured for LAMP via the installer, and I ran aptitude to get all the latest updates and install phpadmin.

This is a Virtualbox VM, Windows 7 x64 as host OS.

When I built it, the VM had one network adapter in NAT mode. After updating everything, I shut down the VM and changed network adapters so that:
-Adapter 1 is "Host-only Adapter"
-Adapter 2 is NAT
(VirtualBox starts adapter numbering at 1.)

Here's the problem: when I booted it back up, the first adapter was working correctly in host-only mode--my VM host could talk with the VM and vice versa.

The second adapter doesn't work at all. If I do "sudo lshw -C network", it shows that there is indeed a 2nd adapter but that it's disabled. If I do "sudo ifup eth1", it says "Ignoring unknown interface eth1=eth1".

How do I get this 2nd adapter to work?