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Coronal holes and active regions are typical magnetic structures found in the solar atmosphere. We propose several magnetohydrostatic equilibrium solutions that are representative of these structures in two dimensions. Our models include the effect of a finite plasma-$β$ and gravity, but the distinctive feature is that we incorporate a thermal structure with properties similar to those reported by observations. We developed a semi-analytical method to compute the equilibrium configuration. Using this method, we obtain cold and under-dense plasma structures in open magnetic fields representing coronal holes, while in closed magnetic configurations, we achieve the characteristic hot and over-dense plasma arrangements of active regions. Although coronal holes and active regions seem to be antagonistic structures, we find that they can be described using a common thermal structure that depends on the flux function. In addition to the force balance, the energy balance is included in the constructed models using an a posteriori approach. From the two-dimensional computation of thermal conduction and radiative losses in our models, we infer the required heating function to achieve energy equilibrium. We find that the temperature dependence on height is an important parameter that may prevent the system from accomplishing thermal balance at certain spatial locations. The implications of these results are discussed in detail.