One step you can start with is to reformulate the system as well as the boundary conditions for the six functions which are the real and imaginary parts of
$A_s(x)=A^{1}_s(x)+i A^2_s(x), A_p(x)=A^1_p(x) + i A^2_p(x)$, and
$B(x)=B^1(x)+iB^2(x)$. Is the independent variable
$x$ real or it is complex?
