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The Documentation shows the proper processing procedure for sub-parts in polygons:

for row in arcpy.da.SearchCursor(infc, ["OID@", "SHAPE@"]):
    # Print the current multipoint's ID
    #
    print("Feature {}:".format(row[0]))
    partnum = 0

    # Step through each part of the feature
    #
    for part in row[1]:
        # Print the part number
        #
        print("Part {}:".format(partnum))

        # Step through each vertex in the feature
        #
        for pnt in part:
            if pnt:
                # Print x,y coordinates of current point
                #
                print("{}, {}".format(pnt.X, pnt.Y))
            else:
                # If pnt is None, this represents an interior ring
                #
                print("Interior Ring:")
        partnum += 1

Note the if pnt test, with the comment

If pnt is None, this represents an interior ring

Some comments:

• Your inner loop is so inefficient, I can't copy it in good conscience. This should be a simple matrix or sparse dictionary of arrays, populated once above the top of the code.

• It should be a crime (misdemeanor data abuse) to not use the spatial_reference parameter in the arcpy.Polygon constructor -- failure to do so will truncate your coordinates to the third decimal place.

• The with construct deletes variables, so your del statements were no-op.

And the corrected code block:

desc = arcpy.Describe(polygon_fc)
sr = desc.spatialReference
with arcpy.da.UpdateCursor(polygon_fc, my_field) as myUpdtCur:
    for row in myUpdtCur:
        geom = row[0]
        arr_pol = arcpy.Array()
        for part in geom:            
            arr_part = arcpy.Array()
            pnt_count = 0
            for pnt in part:
                if not pnt: 
                    continue     # <-- Skips hole markers
                ## assign updZpnt here
                pnt_count += 1                
                print pnt_count
                myXYZPoint = arcpy.Point(pnt.X, pnt.Y, updZpnt)
                arr_part.add(myXYZPoint)
            arr_pol.add(arr_part)

        row[0] = arcpy.Polygon(arr_pol,sr, True)
        myUpdtCur.updateRow(row)