1. S V --- dO -----
They elected his chairman.
2. S V iO dO
They elected him chairman
The first sentence is strange. It is a little hard to imagine the scenario, but clearly "chairman" is the direct object.
In the second sentence "chariman" is an objective complement. You could insert the words "to be" between "him" and "chairman", which might make it a little clearer. Would you like me to Reed-Kellogg the two sentences?