Instead of
%comspec% /c h:\Git\bin\sh.exe --login -i
try to run it with:
%comspec% /c h:\Git\bin\rxvt.exe -e /bin/sh --login -i
And set the environment accordingly, e. g. in .bashrc
:
case $TERM in \
'') export TERM=${TERM:-xterm};; \
esac
etc.