This paper addresses the challenge that current event-based video reconstruction methods cannot produce static background information. Recent research has uncovered the potential of event cameras in capturing static scenes. Nonetheless, image quality deteriorates due to noise interference and detail loss, failing to provide reliable background information. We propose a two-stage reconstruction strategy to address these challenges and reconstruct static scene images comparable to frame cameras. Building on this, we introduce the URSEE framework, the first unified framework designed for reconstructing motion videos with static backgrounds. This framework includes a parallel channel that can simultaneously process static and dynamic events, and a network module designed to reconstruct videos encompassing both static and dynamic scenes in an end-to-end manner. We also collect a real-captured dataset for static reconstruction, containing both indoor and outdoor scenes. Comparison results indicate that the proposed approach achieves state-of-the-art reconstruction results on both synthetic and real data.