The generic method of saving iptables rules is to use the command iptables-save, which writes to stdout.

iptables-save > /etc/network/iptables.rules

As root, issue the command:

iptables-save > /etc/iptables.rules

In /etc/network/if-pre-up.d/iptables put:

#!/bin/sh
iptables-restore < /etc/iptables.rules
exit 0

In /etc/network/if-post-down.d/iptables put:

#!/bin/sh
iptables-save -c > /etc/iptables.rules
if [ -f /etc/iptables.rules ]; then
  iptables-restore < /etc/iptables.rules
fi
exit 0

Give permission to the scripts:

sudo chmod +x /etc/network/if-post-down.d/iptables
sudo chmod +x /etc/network/if-pre-up.d/iptables

The output created by iptables-save can then by read on stdin by iptables-restore.

If on a server, without NetworkManager, a common approach is then to use a pre-up command in /etc/network/interfaces.

iface eth0 inet static
        ....
        pre-up iptables-restore < /etc/network/iptables.rules

NOTE: Do note that the commands iptables, iptables-save and iptables-restore are IPv4 only. For IPv6 traffic the equivalent commands are ip6tables, ip6tables-save and ip6tables-restore.