Its not much true that half monopole is balanced antenna.
Balanced antenna means that the excitation has a phase difference of 180 degrees between his feeds, just like a dipole.
In monople, you only have to excite one feed by a source which referenced to a gorund plane of the monopole antenna, and this is more suitable for an unbalanced case.
The earlier comments about balanced and unbalanced antennas are correct. I think of a balanced antenna as one that has symmetric parts.
I noted in your post that you were asking about a half wave monopole. Usually, people build dipoles with half wavelength spans, tip to tip and monopoles at a quarter wavelength. One can make monopoles work at longer lengths but it is not usually encountered. Just thought I would make that comment.