© 2018 American Physical Society. Multistage coupling of laser-wakefield accelerators is essential to overcome laser energy depletion for high-energy applications such as TeV-level electron-positron colliders. Current staging schemes feed subsequent laser pulses into stages using plasma mirrors while controlling electron beam focusing with plasma lenses. Here a more compact and efficient scheme is proposed to realize the simultaneous coupling of the electron beam and the laser pulse into a second stage. A partly curved channel, integrating a straight acceleration stage with a curved transition segment, is used to guide a fresh laser pulse into a subsequent straight channel, while the electrons continue straight. This scheme benefits from a shorter coupling distance and continuous guiding of the electrons in plasma while suppressing transverse beam dispersion. Particle-in-cell simulations demonstrate that the electron beam from a previous stage can be efficiently injected into a subsequent stage for further acceleration while maintaining high capture efficiency, stability, and beam quality.