A model of the solar chromosphere that consists of two fundamentally different regions, a lower region and an upper region, is proposed. The lower region is covered mostly by weak locally closed magnetic field and small network areas of extremely strong, locally open field. The field in the upper region is relatively uniform and locally open, connecting to the corona. The chromosphere is heated by strong collisional damping of Alfvén waves, which are driven by turbulent motions below the photosphere. The heating rate depends on the field strength, wave power from the photosphere, and altitude in the chromosphere. The waves in the internetwork area are mostly damped in the lower region, supporting radiation in the lower chromosphere. The waves in the network area, carrying more Poynting flux, are only weakly damped in the lower region. They propagate into the upper region. As the thermal pressure decreases with height, the network field expands to form the magnetic canopy where the damping of the waves from the network area supports radiation in the whole upper region. Because of the vertical stratification and horizontally nonuniform distribution of the magnetic field and heating, one circulation cell is formed in each of the upper and lower regions. The two circulation cells distort the magnetic field and reinforce the funnel-canopy-shaped magnetic geometry. The model is based on classical processes and is semi-quantitative. The estimates are constrained according to observational knowledge. No anomalous process is invoked or needed. Overall, the heating mechanism is able to damp 50% of the total wave energy.