The "amniotic sac" that everyone refers to is actually made up of two layers. There is an outer layer called the Chorion and an inner layer called the Amnio layer.
Most twins, be they identical or fraternal, will have their own Amnio layer or membrane.
Fraternal twins will have their own outer, Chorion layer as well because they developed from two separate eggs.
Identical twins could be in their own Chorion layers too, if the egg split very early on.
But, most often, identicals split a little later and share that Chorion layer while they still develop their own inner Amnio layer. Our Dr. explained it as they are sharing an apartment, but still have their own bedrooms.
Occasionally, identical twins who split much later, end up sharing both the Chorion AND the Amnio layer. This isn't ideal and can lead to complications such as conjoined twins.
So, our Dr. thinks the boys are identical because the membranes separating them are so thin that she struggles to see it on the ultrasound. This means that they have their own Amnio layer, but probably share a Chorion layer. If they each had both, the membrane would be thicker and easier to see on the monitor. So, for all you med. students out there, our twins are probably Diamnionic Monochorionic (two Amnios, one Chorion).
Hope this clears up confusion and doesn't add to it!!