When typhoons make landfall in the near-shore area, they usually induce extreme marine environment, such as strong winds and waves, which, as the main environmental loads on bridges across the sea, bring great challenges to the safe operation of bridges in terms of their extremity and complexity. To study the dynamic response characteristics of sea-crossing bridges under extreme wind and wave environments, this paper constructs a reasonable marginal distribution model of wind speed and significant wave height and their Copula joint probability distribution model based on the measured wind and wave data at the bridge site during typhoon. With a sea-crossing bridge as an example, the extreme dynamic response of the sea-crossing bridge under different combinations of wind and wave parameters is calculated in the frequency domain by the spectral decomposition and modal superposition method, where the input pulsating wind spectrum is the Von Karmen spectrum, and the wave spectrum is the P-M spectrum. The structural response surface is constructed, and the structural dynamic response of the sea-crossing bridge under extreme wind and wave environments is analyzed by combining the environmental contours of the joint cumulative distribution of wind speed and significant wave height. The results show that during the typhoon "Dujuan", the maximum wind speed reached 26.1 m/s, and the maximum significant wave height reached 3.15 m at the bridge site. The optimal Copula joint probability distribution model of wind speed and significant wave height is the Clayton model. The maximum root mean square (RMS) of vertical displacement of the bridge mid-span is 2.72 cm, and that is 1.18 cm for the lateral displacement of the tower top and 193 kN for the lateral internal force of the pile foundation when the cumulative probability of wind speed and significant wave height is 0.98 during the typhoon "Dujuan". The displacement response of the main girder is mainly controlled by the wind load; the lateral displacement response of the tower top is controlled by the wind load and the wave load; the lateral internal force response of the pile foundation is mainly controlled by the wave load. The research methodology and conclusions can provide a reference for the design, operation, and maintenance of sea-crossing bridges.