There's a couple ways to whip this llama:
1) Attach two IPs to the Linode, and run Apache bound to one IP and nginx bound to the other.
2) Use one IP address, have one of the web servers listen on port 80, and have it proxy requests for the other one.
3) Use one web server (and one IP) for both sites.
4) Buy a second Linode!
My personal implementation is a combination of #3 and #4... my busy web site runs on its own Linode, with lighttpd+Python wsgi+memcached+postgresql, and everything else runs on a "shared" Linode with lighttpd and a fastcgi handler for each application.