It looks like all the deleted scenes are on the Blu-Ray, not on the DVD.
But yeah, they are in their own section, not part of the main movie. And from what I've seen of them, it's a good thing that they are not part of the main movie. There's some fun stuff in there, but it doesn't really fit with the rest.
I could be wrong about all that. We got the Blu-Ray/DVD set, but I don't have a Blu-Ray player. So I'm just going by the listings on the box. And the deleted scenes that I have seen have just been on the internet. I have not seen the Capt. America scenes that you're talking about. I've seen some SHIELD stuff and some Hulk stuff.