Inversion of adjunction for rational pairs

Let $(X,D)$ be a pair with $D$ a reduced Weil divisor. Let $H$ be a Cartier divisor on $X$ with no components in common with $D$. Assume that $(H,D\cap H)$ is Du Bois and that $(X\setminus H,D\setminus H)$ is a rational pair. Inversion of adjunction for rational pairs. Then $(X,D)$ is a rational pair. This proposed variant of inversion of adjunction would extend the preceding results, including the case $D=0$, by deducing rationality of the pair on $X$ from Du Bois behavior along $H$ and rationality away from $H$; the text presents it as a statement the authors would like to prove.