<p>A pile–bucket composite foundation effectively addresses deep-water offshore loads by combining the vertical load-bearing capacity of single piles with the lateral resistance of bucket foundations. Addressing the core requirement of assessing the safety of complex loads in the design of pile–bucket composite foundations for offshore wind power, this study focuses on a critical operational condition on the horizontal–moment (<i>H</i>:<i>M</i>) bearing capacity–failure envelope while restricting the rotation of the foundation to allow only pure horizontal displacement (<i>H</i>:<i>M</i> = 1:0). To overcome computational complexity in existing numerical methods, this study establishes the upper bound solution of the maximum horizontal translational ultimate bearing capacity for foundations without rotation, using the upper bound approach in limit analysis. This study first conducts small-scale model tests to validate a numerical model; thereafter, based on the validated numerical model, this study analyzes soil potential failure mechanisms in composite foundations at different length-to-diameter ratios; finally, using plastic limit analysis theory, this study establishes a permissible velocity field, derives the upper limit solution formula for the maximum horizontal translational ultimate bearing capacity of pile–bucket composite foundations, and discusses the energy dissipation rate contribution of each component. The upper bound solution calculated values exhibit acceptable errors relative to experimental results, indicating the validity of the upper bound solution formula. This study provides an important theoretical support for determining the critical conditions of the entire <i>H</i>–<i>M</i> failure envelope of pile–bucket composite foundations; it also provides a reference for the design of the horizontal translational bearing capacity of composite foundations.</p>