The sample point error analysis and the related adaptive boundary refinement, proposed by one of the present authors, are extended to problems with subregion partition, which is often required for higher accuracy and for dissimilar materials. Interface between the two subregions should be discretized to raise accuracy of the entire calculation by the boundary integral equations for each subregion combined by using the compatibility and equilibrium conditions. A parameter regularizing the difference between influene of the boundary error is introduced. Two examples are tested to verify the availability of the proposed method.