= Solution
Let $\widehat n$ be the unit normal pointing from the minus medium to the plus medium. Integrating the <Maxwell equations> across an infinitesimal pillbox or loop gives the <dielectric-interface boundary conditions>
$$
\boxed{\widehat n\cdot(D_+-D_-)=0},
\qquad
\boxed{\widehat n\cdot(B_+-B_-)=0},
$$
and
$$
\boxed{\widehat n\times(E_+-E_-)=0},
\qquad
\boxed{\widehat n\times(H_+-H_-)=0}.
$$
Thus tangential $E$ and $H$ are continuous, as are normal $D$ and $B$.
Because $D=\epsilon E$, the normal electric field generally jumps according to
$$
\epsilon_+E_{+,n}=\epsilon_-E_{-,n}.
$$
The tangential displacement field generally jumps because $\epsilon_+\ne\epsilon_-$. Since the permeability is common, continuity of tangential $H$ is continuity of tangential $B$; together with normal-$B$ continuity, every component of $B$ is continuous. The same common $\mu$ also makes the normal component of $H$ continuous.
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