This study presents a design-oriented computational framework for the nonlinear stability assessment of hybrid three-layer timber beams under a uniformly distributed transverse load, composed of high-stiffness face layers and a compliant core, with particular emphasis on the influence of geometric imperfections and interface slip on structural performance. The formulation is developed within a variational energy framework based on the principle of minimum total potential energy, incorporating bending, membrane, and interlayer slip effects under large geometric imperfections, and is solved directly from the governing equilibrium equation rather than through a load-amplification approximation. Extending a previously validated point-load formulation to this practically relevant loading case, an energy-based indicator is employed to interpret the evolution of structural response from bending-dominated behavior to membrane-influenced behavior under increasing deformation. The numerical implementation is carried out using an incremental–iterative procedure, enabling efficient parametric investigation of imperfection amplitudes and interface stiffness levels. The results demonstrate that geometric imperfections trigger early membrane (catenary) engagement and a pronounced hardening of the tangent stiffness from the onset of loading, while simultaneously producing a knock-down in the load capacity available before a fixed serviceability deflection limit is reached. In parallel, a strength-governed demand-capacity criterion reveals an opposite trend, in which pre-curved beams sustain a higher load before reaching the material strength limit, highlighting a genuine design trade-off between serviceability and strength limit states. In addition, large deflections promote the increasing contribution of membrane action, which influences the post-critical structural response. Parametric analyses are conducted to establish relationships between imperfection magnitude, interface stiffness, and stability limits. The obtained results provide design-oriented insights by identifying practical stability thresholds beyond which conventional linear design approaches may become unconservative. The proposed framework therefore offers a computationally efficient tool for the preliminary stability assessment and practical evaluation of hybrid timber members.