Our universe (and there may well be many more universes besides our own) isn't infinite, but there also isn't anything "outside" the universe - the universe is defined as space itself, but space itself has been expanding since the Big Bang. There's no "empty space" outside the universe it's expanding into, though.
I realize it all makes your brain hurt...try reading any of the books from Brian Greene or Michio Kaku.
There may be other universes, but by "the universe" astronomers and physicists mean all the matter (and the space it occupies) that we will ever be able to see, know about or communicate with. According to our current understanding of the laws of nature, if other universes exist there is no way for light, or anything else, to travel from them to us, or any part of our universe, or we to them.
It is a consequence of the theory of General Relativity that our Universe is finite, but it does not exclude the possibility of other universes.
The reason it makes your brain hurt is that it does't make sense. Space is space. Nothingness is space too. Why can't the scientists just use the magic words: "I DON'T KNOW!"?
This is my universe. There are many others like it, but this one is mine. Without my universe, I am nothing. Without me, my universe is nothing.