  Frames formed by orbits of vectors through the iteration of a bounded
operator have recently attracted considerable attention, in particular due to
its applications to dynamical sampling. In this article, we consider two
commuting bounded operators acting on some separable Hilbert space $\mathcal
H$. We completely characterize operators $T$ and $L$ with $TL=LT$ and sets
$\Phi\subset \mathcal H$ such that the collection $\{T^k L^j \phi: k\in \mathbb
Z, j\in J, \phi \in \Phi \}$ forms a frame of $\mathcal H$. This is done in
terms of model subspaces of the space of square integrable functions defined on
the torus and having values in some Hardy space with multiplicity. The
operators acting on these models are the bilateral shift and the compression of
the unilateral shift (acting pointwisely). This context includes the case when
the Hilbert space $\mathcal H$ is a subspace of $L^2(\mathbb R)$, invariant
under translations along the integers, where the operator $T$ is the
translation by one and $L$ is a shift-preserving operator.
