Tangential magnetic field jump from a free surface current
= Tangential magnetic field jump from a free surface current
With interface normal from medium 1 to medium 2, Ampère's <boundary condition> is $\hat{\mathbf n}\times(\mathbf H_2-\mathbf H_1)=\mathbf K_f$. With no free surface current, tangential $H$ is continuous. Normal $B$ is continuous independently because magnetic monopoles are absent.