What is the risk in implementing the NetBEUI protocol in conjunction with the native TCP/IP protocol between an internal network & an outside party?
If you do it right, the risks can be minimal. Assuming you use some sort of firewall to filter traffic, you'll need to open a port on the firewall for NetBIOS over TCP/IP (which is different from NetBEUI, but I'll assume that's what you meant). If you're using a firewall, be sure to configure the port to allow traffic only on TCP port 139 (for NetBIOS over TCP/IP) and TCP port 445 (for CIFS, which more recent versions of Windows use), and only from your partner's source IP address.
If you're not using a firewall, then you're already exposed, and creating a NetBIOS session won't create any additional risk...but you should get a firewall immediately.