This investigation is based on Halpha observations of high spatial resolution. They stem from an enhanced network region near disk centre of the sun and consist of broad-band and narrow-band images taken with the two-dimensional "Gottingen" Fabry-Perot spectrometer mounted in the Vacuum Tower Telescope at the Observatorio del Teide/Tenerife. The "lambdameter method" was applied to derive intensity and velocity maps over the two-dimensional field of view reflecting the behaviour of these parameters in the solar chromosphere. The determination of the source function, the line-of-sight (LOS) velocity, the Doppler width and the optical depth was based on Beckers' cloud model (Beckers 1964). From the LOS velocity distribution along the Halpha structures we conclude that ballistic motions are unlikely to prevail. Especially the bright Ha features cannot be explained by the cloud model. It is shown how, instead, two-dimensional non-LTE radiative transfer calculations of embedded chromospheric structures lead to reasonable agreement with the observed line profiles from these bright features. It is found that many of the bright fibril-like structures near dark fibrils can be explained by radiation which is blocked by absorbing material at large heights and escapes through less opaque regions. We estimate the number densities and the temperature. With these and with the measured velocities, the kinetic energy flux and the enthalpy flux related to the motions of the fine structures can be calculated. Both fall short by at least an order of magnitude of covering energy losses by radiation of active chromospheric regions.