In this work, we studied the behavior of charged microgels at a liquid-liquid interface by means of dissipative particle dynamics simulations with explicit electrostatic interactions; the liquids represent polar and nonpolar solvents like water and oil. The effect of the fraction of charged groups and both solvents qualities on the microgel size, shape, degree of immersion into different liquids, and 2D ordering of the microgels at the interface is studied. For the case of both athermal solvents, we demonstrated that increasing the fraction of charged units results in significant swelling of the microgel inside the polar liquid and a dramatic drop in the number of adsorbed monomer units. For the case of a bad nonpolar solvent for the polyelectrolyte microgels, they easily get detached from the surface into the polar solvent. When the opposite case of a bad polar solvent is considered (like high temperatures for thermosensitive PNIPAM- or PVCL-based microgels), the microgels demonstrate a decrease of the swelling perpendicular to the interface at lows chi-values, and they start to swell into the nonpolar liquid at high chi-values. Two approaches for accounting for different dielectric permittivity of the liquids were considered: implicit and explicit ones; we obtained that the results of the two approaches were always in qualitative agreement. However, the explicit model is necessary to correctly reproduce the physics of the phenomena in certain regimes, in particular, when the charged molecules move through the interface of two liquids. Finally, the microgels ordering was studied at the liquid-liquid interface. We found that even at rather low fraction of charged monomer units the microgels exhibit an almost ideal hexagonal packing even though the average distance between the microgels centers is significantly larger than the microgel diameter, while uncharged microgels positions were completely random. This implies that the interfacial ordering can be controlled by using pH-sensitive monomer units in the microgel structure.