You absolutely can be enlisted in the military AND attend college.

I was planning on joining the Navy, before being medically disqualified, while I was enrolled in college. The Navy told me that I would have to put my education on hold. I had qualified for naval intelligence, so I would have had to go through basic, and then through officer school. After which they would then send me to finish my degree program and complete any other degree programs specifically related to the intelligence sector.

If I recall correctly, going this route would have required me to enlist for a minimum of ten years with nearly half of the time spent on schooling.