To improve the economic efficiency of urban integrated energy systems (UIESs) and mitigate day-ahead dispatch uncertainty, this paper presents an interconnected UIES and transmission system (TS) model based on distributed robust optimization. First, interconnections are established between a TS and multiple UIESs, as well as among different UIESs, each incorporating multiple energy forms. The Bregman alternating direction method with multipliers (BADMM) is then applied to multi-block problems, ensuring the privacy of each energy system operator (ESO). Second, robust optimization based on wind probability distribution information is implemented for each ESO to address dispatch uncertainty. The column and constraint generation (C&CG) algorithm is then employed to solve the robust model. Third, to tackle the convergence and practicability issues overlooked in the existing studies, an external C&CG with an internal BADMM and corresponding acceleration strategy is devised. Finally, numerical results demonstrate that the adoption of the proposed model and method for absorbing wind power and managing its uncertainty results in economic benefits.