This citation/bibliography set-up is slightly confusing in that it may be harder to match citation labels to bibliography entries. A reader will only have the author(s) and year of a work to go on when she consults the bibliography. But in a "
notes" bibliography the year is not in the prominent place at the beginning of the entry, instead it comes near the end, especially in entries with several lines one can get lost trying to find the year. With the "
authordate" bibliography style the year also comes at the beginning and it is much easier to match citation labels to bibliography entries.
Anyway, the styles of the
biblatex-chicago bundle are not supposed to be mixed and matches in this way. There are far too many interdependencies between the bibliography style (
.bbx file) and citation style (
.cbx file), on the other hand there are incompatibilities between the bibliography and citation styles of different substyles, so there is almost no hope of loading and then overwriting a style. In only see two options to resolve this (1) undefine all problematic macros before loading the new style or (2) copy only the relevant bits of both styles into a new style. Both options are doable, but extremely tedious due to the fact that
biblatex-chicago's style files weigh in at several thousand lines of code each.
If you insist on this slightly confusing mix of styles, I recommend you look at
windycity is a more recent implementation of Chicago Style and its structure gives easier access to the output you want. Note that while the general output of
windycity is quite similar, there will be small (and maybe even larger) differences between two.