The boundary of the Milnor fiber of the singularity f(x,y) + zg(x,y) = 0

Let $f,g\in \mathbb{C}\{x,y\}$ be germs of functions defining plane curve singularities without common components in $({\mathbb{C}}^2,0)$ and let $\mathrm{\Phi }(x,y,z)=f(x,y)+zg(x,y)$. We give an explicit algorithm producing a plumbing graph for the boundary of the Milnor fiber of $\mathrm{\Phi }$ in terms of a common resolution for $f$ and $g$.