Interbreath interval (IBI), the time interval between breaths, is an important measure used to analyze irregular breathing patterns in neonates. The discrete bursts of neural activity generate the IBI time series, which exhibits stochastic as well as deterministic dynamics. To quantify the irregularity of breathing, we propose a point process model of IBI using a comprehensive stochastic dynamic modeling framework. The IBIs of immature breathing patterns exhibit a long tail distribution and within a point process model, we have considered the lognormal distribution to represent the stochastic IBI characteristics. An autoregressive (AR) function is embedded within the model to capture the short-term IBI dynamics including abrupt IBI prolongations related to sporadic and periodic apneas that are common in neonates. We tested the utility of our paradigm for depicting the respiratory dynamics in neonatal rats and in preterm infants. Kolmogorov-Smirnov (KS) and independence tests reveal that the model accurately tracks the dynamic characteristics of the signals. In preterm infants, our model-derived indices of IBI instability strongly correlate with clinically derived indices of maturation. Our results validate a new class of algorithms, based on the point process theory, for defining instantaneous measures of breathing irregularity in neonates.