In general, the software reliability models based on the non-homogeneous Poisson processes (NHPPs) are quite popular to assess quantitatively the software reliability and its related dependability measures. Nevertheless, it is not so easy to select the best model from a huge number of candidates in the software testing phase, because the predictive performance of software reliability models strongly depends on the fault-detection data. The asymptotic trend of software fault-detection data can be explained by two kinds of NHPP models; finite fault model and infinite fault model. In other words, one needs to make a hypothesis whether the software contains a finite or infinite number of faults, in selecting the software reliability model in advance. In this article, we present an approach to treat both finite and infinite fault models in a unified modeling framework. By introducing an infinite server queueing model to describe the software debugging behavior, we show that it can involve representative NHPP models with a finite and an infinite number of faults. Further, we provide two parameter estimation methods for the unified NHPP based software reliability models from both standpoints of Bayesian and non-Bayesian statistics. Numerical examples with real fault-detection data are devoted to compare the infinite server queueing model with the existing one under the same probability circumstance.