Realizing Morse functions on orientable surfaces as height functions.

Question

Let $\Sigma$ be an orientable compact surface and let $f : \Sigma \to \mathbb{R}$ be a Morse function. Let $h : \mathbb{R}^3 \to \mathbb{R}$ be the standard height function. Is there an embedding $i : \Sigma \to \mathbb{R}^3$ so that $h \circ e = f$.

I am asking how this works for surfaces in $\mathbb{R}^3$ but I would be interested to know any general results.