Setting zorder for twinx plots

We are trying to plot a climogram (where you have temperature on the
left hand axis, and precipitation on the RHS). The data need to be
properly scaled as well. We have used twinx() to get the two axes.
However, the precipitation (plotted as bars) goes over the temperature
line, when it should be the other way around. I have tried setting the
zorder of the temperature line to a large value, but to no avail. I
have also tried setting the zorder of the axis of the first plot, but
again, no luck.

How can we plot the lines (belonging to the LHS axis) on top of the bars?