[exim] HELO eth1

I have a serverthat is connected to two different subnet, on two different
domains, on two tifferent ISP [actually the thing is wanted, to have more
"network availability"].
Usually it uses the official network on eth0.
If this is not workink however connections are routed throught et1.
I have noticed seeing some message sent this way that the server on helo
give always is "official" domain name, that is hostname.sub.domain.it even if it
uses eth1 that is mx.domain.net
(Incidentally: reverse DNS for eth0 address point to hostname.domain.it, while
for eth1 point to a different thing ( 88-dsl.net216.backupisp.net )
So i ask: is correct to keep this behaviour, even if 90% of messages are
actually routed throught eth1 ?
Should it announce as mx.domain.net (whose dns A record point to eth1
address) or 88-dsl.net216.backupisp.net to match reverse DNS ? (but this
actually would break things when it send trought eth0) .
Is there a way on exim 4.xx to have the helo matching actual IP used to
connect ?
I noticed that messages pass thought anyway, even on fussiest mail servers,
but i ask if there is a cleaner way ...