Setting up VPN on CISCO ASA with private IP on outside interface

I am trying to setup our ASA 5510 to allow IPsec(IKEv1) access to the inside network through VPN. The hard part about our setup is the outside interface does not have a public IP address assigned to it.

Current setup:
Router -> ASA

In between the Router and ASA is a private network. All public IPs are assigned from the ASA to the host on the DMZ.

So I first attempted setting up one of the free public IPs on the ASA. This was setup with a sub interface of 2 and vlan 1 on the outside interface. Then I setup VPN to work over the new interface and that didn’t seem to work.
So I wasn’t sure what the best way of setting up remote VPN access with the ASA when the ASA doesn’t have any public IPs. Any thoughts would be very helpful.