The synchronous firing of neurons in a pulse-coupled neural network composed of excitatory and inhibitory neurons is analyzed. The neurons are connected by both chemical synapses and electrical synapses among the inhibitory neurons. When electrical synapses are introduced, periodically synchronized firing as well as chaotically synchronized firing is widely observed. Moreover, we find stochastic synchrony where the ensemble-averaged dynamics shows synchronization in the network but each neuron has a low firing rate and the firing of the neurons seems to be stochastic. Stochastic synchrony of chaos corresponding to a chaotic attractor is also found.