I had to run a second network interface only for https and this is howto do it:

  1. Edit /etc/network/interfaces as root and change the eth1 configuration to look like this:

auto eth1 iface eth1 inet dhcp post-up ip route add default via route -n |grep UG |awk '{print $2}' dev eth1 table 10001 post-up ip rule add from lookup 10001

  1. Run the following command to prevent DHCP from adding the default gateway for eth1:

sudo su - cat > /etc/dhcp/dhclient-enter-hooks.d/restrict-default-route case in eth0) ;; *) unset new_routers ;; esac EOF CONF

  1. Restart the network configuration by executing the following command: sudo service networking restart

Now you should be able to connect using the second interface public IP.