Highway bridges are critical components of the lifeline transport infrastructure in urban areas. They are designed with the expectation of not sustaining significant structural/non‐structural damage after major earthquake‐induced ground shaking. However, in the current structural performance‐based assessment practice, the effects of a pre‐damaged state during ground‐motion sequences are often neglected. Additionally, environmentally induced deterioration mechanisms (e.g., steel rebar corrosion) may exacerbate the consequences of such ground‐motion sequences on the seismic structural performance during the bridge design lifetime; yet such effects are commonly overlooked. This study proposes a computational methodology to derive state‐dependent fragility and vulnerability relationships (i.e., explicitly depending on the damage state achieved by the bridge structure during a first shock) for bridge structures subjected to chloride‐induced corrosion deterioration and ground‐motion sequences. The methodology is demonstrated for a case‐study ordinary bridge structure (representing a typical bridge vulnerability class in southern California) under seismic sequences assembled from the CyberShake 15.12 (hybrid) simulated ground‐motion database. In the proposed approach, parameterised (i.e., dependent on the corrosion deterioration level) vector‐valued probabilistic seismic demand models are developed for the bridge components (i.e., columns and shear keys). These models, calibrated through sequential cloud‐based nonlinear time‐history analyses, relate the dissipated hysteretic energy in the ground‐motion sequence to a deformation‐based engineering demand parameter induced by the first shock and a ground‐motion intensity measure of the second shock for a given corrosion deterioration level. Fragility relationships are first derived for a single ground motion at the component‐level; state‐dependent fragility relationships are then derived by considering the additional damage induced by a second ground motion within the simulated sequence (structure‐specific damage states are considered). Furthermore, a component‐based simulation approach accounting for the correlations across the components’ response is utilised to derive fragility relationships at the system level (i.e., for the bridge structure). Finally, appropriate damage‐to‐loss models for ordinary bridges are used to derive state‐dependent vulnerability relationships. The results demonstrate the significant impact of earthquake‐induced ground‐motion sequences and environmentally‐induced corrosion deterioration, emphasising the necessity of accounting for this multi‐hazard threat in the structural performance‐based assessment of bridges. Relative variations up to 120% can be found in the system‐level state‐dependent fragility median values comparing the results for the bridge in pristine and deteriorated conditions.