Line is covered by PlotMarkers in ListLinePlot

Suppose I plot the data and fitting line with black point and red line

imgPlotMarkers00 =  ListLinePlot[{Range[60] + RandomReal[{-1, 1}/2, 60], Range[60]},  PlotMarkers -> {Automatic, None}, PlotStyle -> {Black, Red},  Joined -> {False, True}] 

However, I found in the output figure

enter image description here

the black points cover up the red line. How could I move the red line to the top layer of figure? Is their a option for this?

This is a simple example. In real case I have more than one data-fit line pairs to plot and their legends to placed.