Context. Because of the complex physics that governs the formation of chromospheric lines, interpretation of solar chromospheric observations is difficult. The origin and characteristics of many chromospheric features are, because of this, unresolved. Aims. We focus on studying two prominent features: long fibrils and flare ribbons. To model these features, we use a 3D magnetohydrodynamic simulation of an active region, which self-consistently reproduces both of these features. Methods. We modeled the Hα, Mg II k, Ca II K, and Ca II 8542 Å lines using the 3D non-LTE radiative transfer code Multi3D. To obtain non-LTE electron densities, we solved the statistical equilibrium equations for hydrogen simultaneously with the charge conservation equation. We treated the Ca II K and Mg II k lines with partially coherent scattering. Results. This simulation reproduces long fibrils that span between the opposite-polarity sunspots and go up to 4 Mm in height. They can be traced in all lines owing to density corrugation. In contrast to previous studies, Hα, Mg II h&k, and Ca II H&K are formed at similar height in this model. Although some of the high fibrils are also visible in the Ca II 8542 Å line, this line tends to sample loops and shocks lower in the chromosphere. Magnetic field lines are aligned with the Hα fibrils, but the latter holds to a lesser extent for the Ca II 8542 Å line. The simulation shows structures in the Hα line core that look like flare ribbons. The emission in the ribbons is caused by a dense chromosphere and a transition region at high column mass. The ribbons are visible in all chromospheric lines, but least prominent in Ca II 8542 Å line. In some pixels, broad asymmetric profiles with a single emission peak are produced similar to the profiles observed in flare ribbons. They are caused by a deep onset of the chromospheric temperature rise and large velocity gradients. Conclusions. The simulation produces long fibrils similar to what is seen in observations. It also produces structures similar to flare ribbons despite the lack of nonthermal electrons in the simulation. The latter suggests that thermal conduction might be a significant agent in transporting flare energy to the chromosphere in addition to nonthermal electrons.