I learned English in school, but I only became fluent later on in life. When I was around 30, I worked in an English speaking environment and also at home I spoke English. I was thinking in English and there were days that I did was surprised when I heard some Dutch being spoken, suddenly realizing I had been thinking in English all the time. I felt at some time that the two language become one in my mind, that I could effortless switch from on to the other. I also acquired the ability to simultaniously translate from English to Dutch. I even sometimes when I was doing this, would find my mind to wander off, as if it had become a purely automated task. The surprising things is that I am a dyslectic and often have to look up the spelling of words. Dutch spelling seems to give me more trouble than English.
I think that many bilingual people share the same experience, but that it is hard to believe for someone who is not bilingual her/himself to believe that a second (or third) acquired language can be as intergrated as your mother tongue.