Several ultrasonic tissue characterization features are known to discriminate pathological from normal tissue in vivo. Previously, the authors developed an in vivo attenuation- and backscatter estimation method with each frequency dependent coefficient being reduced to a slope and intercept at central frequency. They derived expressions predicting the standard deviation (SD) of these features, assuming a commonly used ultrasonic model of liver parenchyma. In its application to in vivo data, the SD of the intercept features was unexpectedly high. Another feature, signal-to-noise ratio (SNR), showed a significant bias related to the window size. In this paper, the model is extended with the notion of inhomogeneous parenchyma background (IPB). IPB is shown to be present in normal liver parenchyma and is statistically described by a noise term with small amplitude and large correlation cell size. A method is presented to estimate the IPB characteristics. The expressions predicting SD are extended, and an expression is derived predicting the window size bias of the feature SNR. The accuracy and precision estimated from a large in vivo data set shows good agreement with the predictions with the extended model. It is concluded that IPB is a realistic and relevant phenomenon and should be part of the in vivo ultrasonic model of liver parenchyma.