Thin liquid films play a big role in many real-life applications and are of indisputable interest to scientific and industrial researchers. Evidence of thin films are observed in nature in large scales such as snow avalanches in the mountains, lava flows on volcanoes and landslides, and in small scales such as the pulmonary airways and the eye surface. They are also widespread in many industrial applications, ranging from high-resistance thin film resistors, atomization, soft-lithography methods and several coating techniques such as dip, roll, slot, spin and curtain coating. Understanding the physical mechanisms contributing to the stability of thin liquid films is a challenging problem, as thin films flows present a fluid-fluid interface which is free to deform. The interface is bounded between two liquids or a liquid and a gas, typically having its own dynamic properties from which interfacial tension effects and complex interfacial rheological behavior arises. Instability is usually driven by long-range intermolecular forces, also known as van der Waals attractions, and may result in the rupture of the layer. Numerical investigation is often used to understand the breakup dynamics of thin liquid sheets by addressing the evolution of the film thickness using either asymptotic derivations of the lubrication theory or interface tracking techniques. In this work, a computational investigation of the breakup dynamics of a stationary thin liquid sheet bounded by a passive gas with a viscous interface is presented. The Arbitrary Lagrangian-Eulerian method (ALE) is used to track the interface position. The rheological behavior of the viscous interface is modeled by the Boussinesq-Scriven constitutive law, and the numerical solution is obtained through finite element approximation. The results show that thin liquid film stability is influenced both by surface rheology and disjoining effects and that the viscous character of the interface delays the sheet breakup, leading to more stable films.