We study a superconducting hetro-junction with one side characterized by the unconventional chiral $p$-wave gap function $p_xpm ip_y$ and the other side the conventional $s$-wave one. Though a relative phase of $pm frac{pi}{2}$ between any two components of gap functions is favored in the junction region, mutual phase differences cannot achieve $pm frac{pi}{2}$ simultaneously, which results in frustration. Based on a Ginzburg-Landau free energy analysis, the frustrated pattern is determined to be $s+ ieta_1 (e^{ ieta_2 varphi/2}p_x +eta_3 e^{- ieta_2 varphi/2}p_y)$ with $eta_j=pm 1$ ($j=1,2,3$), where $varphi$ is the phase difference between the $p_x$- and $p_y$-wave gap functions. Furthermore, we find that the junction exhibits an anisotropic magnetoelectric effect, manifesting itself as an anisotropic spin magnetization along the edge of the junction.
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