Modeling and simulation play a vital role in the design and testing of modular multilevel converter (MMC) high voltage direct current (HVDC) systems. Detailed equivalent model (DEM) and switching-function-based average value model (SFB-AVM) are two major types of accurate and efficient models to represent the dynamic response of the MMCs. However, the DEM and the SFB-AVM possess unique benefits depending on the purpose of the simulation studies. The DEM provides a detailed representation of submodule (SM) switching events and individual capacitor ripples. The SFB-AVM provides faster simulation speed by using arm equivalent capacitance. Combining both models in a universal arm equivalent circuit gives the users the choice of selecting the most appropriate modeling method during dynamic simulation. This paper proposes a universal modeling framework combining the DEM with the SFB-AVM which allows the DEM and the SFB-AVM smoothly switch from one to the other during dynamic simulation. The proposed SFB-AVM can accurately represent the MMCs with different SM types. The proposed models are validated in offline and real-time simulation studies which demonstrate the improved simulation speeds of the proposed SFB-AVM over the DEM especially for large numbers of SMs.