Epithelial monolayers are two-dimensional cell sheets which compartmentalize the body and organs of multicellular organisms. Their morphogenesis during development or pathology results from patterned endogenous and exogenous forces and their interplay with tissue mechanical properties. In particular, bending of epithelia is thought to result from active torques generated by the polarization of myosin motors along their apicobasal axis. However, the contribution of these out-of-plane forces to morphogenesis remains challenging to evaluate because of the lack of direct mechanical measurement. Here we use epithelial curling to characterize the out-of-plane mechanics of epithelial monolayers. We find that curls of high curvature form spontaneously at the free edge of epithelial monolayers devoid of substrate in vivo and in vitro. Curling originates from an enrichment of myosin in the basal domain that generates an active spontaneous curvature. By measuring the force necessary to flatten curls, we can then estimate the active torques and the bending modulus of the tissue. Finally, we show that the extent of curling is controlled by the interplay between in-plane and out-of-plane stresses in the monolayer. Such mechanical coupling emphasizes a possible role for in-plane stresses in shaping epithelia during morphogenesis.