I reached such a level of immersion that one day I was watching a film with a friend and the actors suddenly switched to Spanish for a while and I didn't notice it, my friend had to tell me!
I remember learning words in English and being unable to give the Spanish equivalent afterwards, but I kept thinking mostly in Spanish, although I was much more fluent in English.
My thought-process is in my native language, but I think in English when I speak the said language. I don't need to translate English to my native language to understand it, either (I don't want to think about it, too much, though - If I try too hard to understand, it isn't as easy).
A good way to practice English is to watch English TV series with subtitles. :)
But dubbing is no help at all - at least, I found it unhelpful when I was watching Spanish TV. The lip movements (in my own language - mostly American films) were too much of a distraction.