Electric vehicles (EVs) are widely recognized as promising solutions to reduce carbon emissions from the transportation sector. The rapid proliferation of EVs intensifies the interdependency between the power distribution system (PDS) and transportation system (TS). This paper proposes a distributed low-carbon economic dispatch scheme for the integrated power and transportation system (IPTS). Carbon emissions from the TS are quantified by a carbon dioxide calculation model, and the emissions from the PDS are determined by the electricity generation of fossil-fueled generators and the carbon reduction of carbon capture and storage (CCS) devices. An integrated model reformulation method is employed to transform the original non-convex model into a tractable one. Then a distributed solution method based on the spectral penalty parameter based adaptive alternating direction method of multipliers (SPPA-ADMM) is developed to protect the privacy of the PDS and TS. The reformulated model is solved iteratively, and the penalty parameter of the SPPA-ADMM is adjusted adaptively to improve the convergence performance of the method. Numerical results on three test systems demonstrate the effectiveness of the proposed scheme in achieving low-carbon economic dispatch of IPTS. Moreover, case studies validate the superiority of the SPPA-ADMM based distributed solution method in computation performance.