Unfortunately, if, for no other reason, because you are not twin rated, you cannot log any multi-time (PIC or otherwise). If he is an MEI (meaning that he is a multi-engine instructor) then on the dead leg, in this case (since it sounds like you're just operating under parts 61 and 91), you could log duel received (and he will need to sign your logbook). However; remember, he must be an MEI. If he is a CFI or CFII, then you still won't be able to log the time.
I think we may be diverging from this forum's intent a tad bit
. Be careful when you ask a CFI a question about flying. You may not be able to get him to shut up!
I really do hope this helps. I'm just telling you the way it is written. It is still good experience to fly in a twin, even you aren't logging time, however.