The stability of a two‐dimensional magnetic model of a thick quasineutral sheet including a small but finite normal magnetic field component is studied in a collisionless plasma. Such a magnetic configuration allows an adiabatic motion for electrons which are trapped in good agreement with the thick sheet model. A detailed kinetic study of the energy balance shows that the ion linear tearing mode instability is suppressed by the interaction between the perturbed electromagnetic field and the adiabatic electron motion; this interaction leads to a ‘‘compressibility’’ effect which prevents the instability onset. The connection with the magnetohydrodynamic energy principle for stability is demonstrated. A general formalism is developed for any magnetic configuration and applied to a parabolic and a magnetic island topology. Some conclusions concerning the nonlinear tearing mode behavior (explosive phase) are drawn.