Finding kinetic equilibria for tangential current layers is a key issue for the modeling of plasma phenomena such as magnetic reconnection, for which theoretical and numerical studies usually aim in starting from steady state current layers. The famous Harris equilibrium is known to be limited to symmetric layers surrounded by vacuum, with constant temperature, and constant ion and electron flow velocities, and with a current variation depending only on the density variation. It is clearly not suited for the modeling of ``magnetopause-like'' layers, which separate two plasmas of different densities and temperatures. In order to understand this kind of boundaries, Belmont et al (2012) presented a new asymmetric equilibrium which was validated in a hybrid simulation by Aunai et al (2013), and more recently in a fully kinetic simulation as well. For this equilibrium to be computed, the magnetic field had to stay coplanar inside the layer. We present here an important generalization, where the magnetic field rotates inside the layer (restricted to a 180° rotation hitherto). The tangential layers so obtained are thus closer to those encountered at the magnetopause. This will be necessary, in the future, for comparing directly the theoretical profiles with the experimental ones for the various physical parameters. As it was done previously, the equilibrium is tested with a hybrid simulation.