Yes it is. You have to setup the router as a reverse proxy and forward HTTP requests to one of the hosts in the private network based on the Host
header or the request URL. Nginx is a popular choice when it comes to reverse proxying.
If you want to proxy services other than HTTP, SMTP or IMAP servers, then you need to use iptables instead, such as
iptables -t nat -A PREROUTING -d $DOMAIN_NAME -j DNAT --to-destination $SERVER2_IP
iptables -t nat -A POSTROUTING -j MASQUERADE