In this paper, we introduce an immersed \(C^0\) interior penalty method for solving two-dimensional biharmonic interface problems on unfitted meshes. To accommodate the biharmonic interface conditions, high-order immersed finite element (IFE) spaces are constructed in the least-squares sense. We establish key properties of these spaces including unisolvency and partition of unity, and verify their optimal approximation capability. These spaces are further incorporated into a modified \(C^0\) interior penalty scheme with additional penalty terms on interface segments. The well-posedness of the discrete solution is proved. Numerical experiments with various interface geometries confirm optimal convergence of the proposed method in \(L^2\) , \(H^1\) and \(H^2\) norms.
