Despite its seemingly specialized name, Computer Engineering is actually a very broad field of study, encompassing virtually all aspects of computing, both theoretical and applied. It was initially created as a branch of electrical engineering as computer technology began to explode in the late eighties and early nineties, but realistically it can't be regarded as a "branch" of anything any longer given the sheer growth of the field in the last decade.
A good Computer Engineering program generally includes (in no particular order):
If I had a say, I would personally add philosophy of science and systems theory to that list, though some may be lucky enough to have those electives available to them.
The unfortunate thing about this field is that it's currently the "sexy" engineering discipline to be in, attracting a disproportionate number of gold diggers looking to strike it IT rich in this "brave new high-tech world". This results in classrooms full of students who care nothing about computing or science in general and are only concerned about how good their Microsoft summer placement will look on their resume.
That aside, Computer Engineering, if fully appreciated, can provide a tremendous foundation for further scientific exploration.