  We study the joint components in a random `double graph' that is obtained by
superposing red and blue binomial random graphs on $n$~vertices. A joint
component is a maximal set of vertices, which contains both a red and a blue
spanning tree. We show that there are critical pairs of red and blue edge
densities at which a joint-giant component appears. In contrast to the standard
binomial graph model, the phase transition is first order: the size of the
largest joint component jumps from $O(1)$ vertices to $\Theta(n)$ at the
critical point. We connect this phenomenon to the properties of a certain
bicoloured branching process.
