Natural gas (NG) network and electric network are becoming tightly integrated by microturbines in the microgrid. Interactions between these two networks are not well captured by the traditional microturbine (MT) models. To address this issue, two improved models for single-shaft MT and split-shaft MT are proposed in this paper. In addition, dynamic models of the hybrid natural gas and electricity system (HGES) are developed for the analysis of their interactions. Dynamic behaviors of natural gas in pipes are described by partial differential equations (PDEs), while the electric network is described by differential algebraic equations (DAEs). So the overall network is a typical two-time scale dynamic system. Numerical studies indicate that the two-time scale algorithm is faster and can capture the interactions between the two networks. The results also show the HGES with a single-shaft MT is a weakly coupled system in which disturbances in the two networks mainly influence the dc link voltage of the MT, while the split-shaft MT is a strongly coupled system where the impact of an event will affect both networks.