Military
Now, despite The Thalmor's obviously racist attitude towards anyone who's not an altmer, they are probably smart enough to allow other races native to their provinces into their military. Though their roles and classes varies depending on their race.
Goblins: If Alinor still practices enslavement of goblins; (I'm pretty sure they still do.) Then they are used to either construct siege equipment, or to be expendable units sent on suicide charges. Nothing more.
Igma: Since they are more or less talking apes who loves The Altmer; they probably serve as The Dominion's shock troopers. In other words, their size and loyalty to The Thalmor gives them enough value to not be wasted. They are unlikely to retreat unless told to and can potentially cause fatal damage when flanking or charging head-on to enemy light infantry.
Khajiit: Khajiit's who fight for the dominion are either part of their client-states in Elsywere's military or in The Actual Dominion's army. Either way, their role varies depending on the sub-species. Though they are generally used as skirmishers or to cause hell behind enemy lines.
Bosmer: This should be easy. While there may be a few odd ones that are infantry; most Wood Elves in Military service are archers. And are the only race that could be archers except for The Altmer and maybe Khajiit. Though given Valenwood's environment and Bosmeri culture, Bosmer soldiers tend to lack disipline.
Altmer: Compare to the other races, The Altmer has it easy in the military. They serve as the bulk of the army and most sailors, save for maybe some Bosmeri archers on ship, are Altmer. They could be infantry, archers, or mages. (So they have a little more options in the army then the other races.)While their archers may not be as skilled as The Bosmer or as numerous, they do make it up for better disipline. And to top it of, almost all officers, save for maybe a few Wood Elves, are High Elves.
Political structure
First we have whoever is in charge of Alinor's cities, they answer to The King, who is then a Thalmor puppet. The Thalmor itself is run by a small and council. While most of this council are Altmer, there are a few represenatives from Valenwood. There is an Altmer governor in Valenwood who directly runs the province. But he also performs orders carried out by the Council. Elsweyre on the other hand, is mostly independent, but must allow Dominion occupation, as well to pay tribute.
So what are your opinions on this? And what is your view of how The AD is organized?