The actors playing the leads make a visible switch on-stage with dancers in identical clothes. The dancers perform the Agnes deMille ballet that recapitualtes the story of the musical up to that point, with a nightmare ending tacked on. That was a necessary switch because ballet is so complex that only dancers can do it. The dream sequence is also clearly marked off as a fantasy. But acting and singing are allied arts, or are supposed to be.
Many singers can also carry their own in an acting part.
A lot of people can do both pretty well. It was also lazy casting. It would be much better to choose a single person to sing and speak, even if her voice was not perfect. Even if she wasn't operatic, people would at least appreciate the effort. Since Disney's musicals have scored so well as soundtrack albums, movie companies have made good money by selling great quantities of soundtrack CD's.