The electrical activity of neurons depends on the physiological conditions in the nervous system. An electromagnetic field, for example, can significantly affect the dynamics of individual neural cells, and it also affects their collective dynamics. It is therefore of interest to study the neuronal dynamics under such an influence in various setups. We thus study the firing patterns in two coupled neurons by considering three different types of synapses, namely electrical, chemical, and electrochemical. We use the Hindmarsh–Rose mathematical model as the basis of neuronal dynamics, and we also introduce an electromagnetic field effect. We conduct extensive calculations of the firing patterns, and we determine the bifurcation diagrams for constant and periodic external currents. The results show that the different synaptic connections evoke different firing patterns and that in general electrochemical synapses can show richer variety of dynamical behavior than electrical or chemical synapses.