  We introduce a class of ideals generated by a set of 2-minors of $m\times
n$-matrix of indeterminates indexed by a pair of graphs. This class of ideals
is a natural common generalization of binomial edge ideals and ideals generated
by adjacent minors. We determine the minimal prime ideals of such ideals and
give a lower bound for their degree of nilpotency. In some special cases we
compute their Gr\"obner basis and characterize unmixedness and
Cohen--Macaulayness.
