Exchange bias has been studied in a series of La2/3Ca1/3MnO3 / La1/3Ca2/3MnO3 bilayers grown on (001) SrTiO3 substrates by ozone-assisted molecular beam epitaxy. The high crystalline quality of the samples and interfaces has been verified using high-resolution X-ray diffractometry and Z-contrast scanning transmission electron microscopy with electron energy loss spectroscopy. The dependence of exchange bias on the thickness of the antiferromagnetic layer has been investigated. A critical value for the onset of the hysteresis loop shift has been determined. An antiferromagnetic anisotropy constant has been obtained by fitting the results to the generalized Meiklejohn-Bean model. Comment: 7 pages. 8 figures