The overlaying music in parallel scenes happens when the music of the first scene is heard in the second. The music appears in the first scene diegetically, and then continuous (non-diegetically) in the second: the audience is aware that it is an overlaying superimposed music.
The narrative result is that the action or characters in the first scene «invade» and control what happens in the second scene.

The music from the Church scene is extended (overlaid) into the scene with the spies in Homeland  1×04. The synchronicity is stressed, and the audience becomes aware that the time of one scene controls the actions in the other

Interwoven scenes with overlaying music from the Church that stresses the power and hypocrisy of the characters over the criminal actions in The Godfather.

Interwoven scenes with overlaying music to stress the synchronicity and alternance in The Hour 2×01 (analysis by Irene Chilet Murgui, student of Análisis de Recursos Sonoros).