First of all, I'm not a shipbuilding engineer, but that design Yours just looks like there is something wrong with it.
Correct me if I'm wrong, but it looks that Your idea is basically a BAP Juan Carlos I, HMAS Canberra or Italian Cavour on steroids crossed with Nimitz, with some elements (strong AAW capability) taken from, say, Soviet Kiev? As (judging by the air group) Your design is made with US Navy in mind, I'd say that - both from doctrinal and practical point of view it's rather poor idea - as some have already pointed out, it's better to separate strike carrier and amphibious assault ship.
The idea is perhaps somewhat more viable if aimed at some smaller (medium-sized) navy, that has bigger ambitions than budget, for operations in moderate-threat environment (like a rerun of the Falklands War, for example).
As for the ship itself - island is waaay to small, and I don't mean that it's not tall enough, but not long enough - take a look on the ships I've already mentioned. Right now, Your island resembles rather late WW2 British aircraft carriers like Colossus class.
Note, that hull of Your ship would have not to just fit the hangar inside, but also lots of space for marines and (most likely) dock for landing craft (unless it's an old-school commando carrier with marines being transported only by helicopters?). Therefore the island probably has to house some things that otherwise could be hidden in the hull (below the flight deck), so it should be apropriately bigger.
Also, what about dock for landing craft? It's there or not - because if it's there, I'm not sure about that stern VLS - is it 2 launchers on both sides of dock entrance, or a single one, as it looks to me that it would simply block the dock (unless it's VERY small one).
