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We investigate the response of magnetic vortex cores in bilayer dots, a vertical stack of disk and square sublayers, to ultrashort in-plane magnetic field pulses by micromagnetic simulations. The bilayer dots adopt the advantage of switching behaviors of constituent dots; the low switching field threshold of the square is still maintained and the operating switching field range is intermediate, compared to the single-layer disk and square. Besides the usual creation and subsequent annihilation of vortex-antivortex pair reported previously, subsequent antivortex or vortex and antivortex pair during the vortex core switching process can be observed in the bilayer dot with a lateral size of about 100 nm. [ABSTRACT FROM AUTHOR]