Buildings are exposed to multiple natural hazards over their service lives. Multihazard analysis and design of building structures has become a research hotspot worldwide. For these structures, earthquake and progressive collapse are two of the most commonly encountered hazards. However, little research has been conducted to examine the effects of the seismic and progressive collapse designs on the resistance of buildings against multiple hazards. In this study, a series of six-story reinforced concrete (RC) frames are considered, and their seismic and progressive collapse designs are performed independently according to the corresponding design codes. Fragility curves are used to assess the seismic and progressive collapse resistance. The interactions between the two designs are discussed by analyzing the fragility curves and the collapse modes. Results show that the progressive collapse design of the RC frame may lead to an undesirable failure mode (i.e., strong-beam-weak-column) under earthquakes, which indicates that a seismic redesign is necessary subsequent to the progressive collapse design. Note that sequential use of different design codes for a structure may result in material waste yet a suboptimal structural performance. Therefore, a design method by individually considering different hazards is unsuitable for the multihazard prevention and mitigation of building structures. A comprehensive and integrated design method for multihazards is thus in great need. The outcome of this study will lay a foundation for future multihazard analysis and design of building structures.