I did some research on this a while back, and I came up with a couple of theoritical ways.
1. Use a PRI to the Avaya PBX for phone calls both ways, and use SMDI to integrate the voicemails (i.e. light the MWI)
2. Use the Unity Bridge to do the translation for you, but this requires a couple of Unity servers and as assumed is a much more "full featured" way of doing the integration.
I'd be interested if someone else found another way to do this.
Rick