BZIP2 looks at a bit stream.
From http://blastedbio.blogspot.com/2011/11/random-access-to-bzip2.html:
Anyway, the important bits are that a BZIP2 file contains one or more "streams", which are byte aligned, each containing one (zero?) or more "blocks", which are not byte aligned, followed by an end of stream marker (the six bytes 0x177245385090 which is the square root of pi as a binary coded decimal (BCD), a four byte checksum, and empty bits for byte alignment).
The bzip2 wikipedia article also alludes to bit-block alignment (see the File Format section), which seems to be inline from what I remember from school (had to implement the algorithm...).