the only way I can reproduce your result, is by rotating the half to be mirror before mirroring (M,X) it; and/or using a misplaced pivot centre. Alternatively, to use a misplaced object as mirror object. As far as I know, it is not possible to achieve your result using the cardinal coordinate axes as mirroring directions.
Note: Judging from your screen shot above, you are not using a mirror modifier. What to use is of course depending on what you want to achieve, by in most cases a mirror modifier is what you use for symmetric objects.