Iptables – Only allow HTTP(S) and DNS using iptables

Currently the NAT host and respective clients are able to access any service. I like the NAT host (the device running IPTABLES) to only be able to access HTTP(S), DNS and send/respond to ICMP requests.

I would like the internal clients behind $INTIF to only access HTTP(S) and DNS. I tried multiport but I had little luck. I'm open to other suggestions.

*nat
-A POSTROUTING -o "$EXTIF" -j MASQUERADE
COMMIT
*filter
:INPUT DROP [0:0]
:FORWARD DROP [0:0]
:OUTPUT DROP [0:0]
-A INPUT -p tcp -i eth1 --dport 22 --sport 1024:65535 -m state --state NEW -j ACCEPT
-A INPUT -i "$INTIF" -p udp --dport 53 -j ACCEPT
-A INPUT -m conntrack --ctstate ESTABLISHED,RELATED -j ACCEPT
-A INPUT -m limit --limit 3/min -j LOG --log-prefix "input denied: " --log-level 7

-A FORWARD -i "$EXTIF" -o "$INTIF" -m conntrack --ctstate ESTABLISHED,RELATED -j ACCEPT
-A FORWARD -i "$INTIF" -o "$EXTIF" -m state --state ESTABLISHED,RELATED -j ACCEPT
-A FORWARD -i "$INTIF" -o "$EXTIF" -m multiport -p tcp --dports 80,443 -j ACCEPT
-A FORWARD -m limit --limit 3/min -j LOG --log-prefix "forward denied: " --log-level 7

-A OUTPUT -m state --state NEW,ESTABLISHED,RELATED -j ACCEPT
-A OUTPUT -m limit --limit 3/min -j LOG --log-prefix "output denied: " --log-level 7
COMMIT