The Madden-Julian Oscillation (MJO) and El Niño-Southern Oscillation (ENSO) are two crucial climate patterns that affect the entire Earth system. While their individual dynamics have been studied separately, their interactions, especially in the presence of different types of El Niño events (varying by location, duration, and strength) with diverse and complex features, have not received enough attention in modeling studies. This paper develops a simple intermediate coupled MJO-ENSO model that is simpler than operational models but more detailed than basic conceptual ones. The explicit spatiotemporal model structures allow the study of how MJO, ENSO, and decadal variability interact. By further incorporating appropriate stochastic components, the model successfully reproduces many observed features of both phenomena, including the ENSO diversity and complexity. It is also statistically accurate, which makes it distinct from many existing models. This new model serves as a practical tool for studying MJO-ENSO relationships under different climate conditions. The computational efficiency and statistical accuracy of this model also allow for generating long simulations, which facilitates the study of extreme events and statistical forecasting, as well as providing sufficient training data for various machine learning tasks.