Im trying to find a characterization of the prime ideals in the polynomial ring $R = \mathbb Z[X,Y]$ in two variables over the integers.

Actually I need to find the maximal ideals in quotient rings $R / I$ where $I$ has codimension 2 such that $R/I$ is free and finitely generated as a $\mathbb Z$-module, i.e. I need to find the maximal ideals $I \subseteq \mathfrak m \subseteq R$. An example of such an $I$ is the ideal generated by $X^2 - XY - Y - 1$ and $X^3 - X^2 - 2XY - X - Y$.

In Mumford's Red Book of Varieties and Schemes, II, §1, Example H there is a characterization of prime ideals in $\mathbb Z[X]$. Do anyone know how to generalize that to two indeterminates?