  In this article we study the scaling limit of the interface model on
$\mathbb{Z}^d$ where the Hamiltonian is given by a mixed gradient and Laplacian
interaction. We show that in any dimension the scaling limit is given by the
Gaussian free field. We discuss the appropriate spaces in which the convergence
takes place. While in infinite volume the proof is based on Fourier analytic
methods, in finite volume we rely on some discrete PDE techniques involving
finite-difference approximation of elliptic boundary value problems.
