The state-of-the-art automatic speech recognition (ASR) systems typically use phonemes as subword units. In this work, we present a novel grapheme-based ASR system that jointly models phoneme and grapheme information using Kullback-Leibler divergence-based HMM system (KL-HMM). More specifically, the underlying subword unit models are grapheme units and the phonetic information is captured through phoneme posterior probabilities (referred as posterior features) estimated using a multilayer perceptron (MLP). We investigate the proposed approach for ASR on English language, where the correspondence between phoneme and grapheme is weak. In particular, we investigate the effect of contextual modeling on grapheme-based KL-HMM system and the use of MLP trained on auxiliary data. Experiments on DARPA Resource Management corpus have shown that the grapheme-based ASR system modeling longer subword unit context can achieve same performance as phoneme-based ASR system, irrespective of the data on which MLP is trained.