  The inside of the electrical double layer at perovskite oxide
heterointerfaces is examined. Here, we report the local polarization and
valence distribution in LaNiO$_3$/LaMnO$_3$ and LaMnO$_3$/LaNiO$_3$ bilayers on
a SrTiO$_3$ (001) substrate. Simultaneous measurements of two aspects of the
structure are realized by using Bayesian inference based on resonant- and
nonresonant-surface X-ray diffraction data. The results show that the average
Mn valences are Mn$^{3.12+}$ and Mn$^{3.19+}$ for the two samples. The
intensity of their local electric field is $\sim$1~GV/m and the direction of
the field points from LaMnO$_3$ to LaNiO$_3$.
