The Kruskal-Szekeres coordinate system is arranged so that the worldlines of radially infalling (yellow) and outgoing (ochre) light rays lie at 45o.
The white hole is the region at the bottom of the diagram, bounded by the two red antihorizons. The black hole is the region at the top of the diagram, bounded by the two pink-red horizons. Both white and black holes have singularities at their centres, the cyan lines. The regions at left and right outside the horizons are the two Universes. The two Universes are joined by a wormhole, the region of spacetime between the white hole and black hole singularities.
As long as the inhabitants of the two Universes remain outside the horizons, they cannot meet or communicate with each other. However, the inhabitants can meet after falling into the black hole. Having met, they also soon meet the singularity.