Cosmic shear is a powerful probe of cosmological parameters, but its potential can be fully utilized only if galaxy shapes are measured with great accuracy. Two major effects have been identified which are likely to account for most of the bias seen for maximum likelihood methods in recent shear measurement challenges. Model bias occurs when the true galaxy shape is not well represented by the fitted model. Noise bias occurs due to the non-linear relationship between image pixels and galaxy shape. In this paper we investigate the potential interplay between these two effects when an imperfect model is used in the presence of high noise. We present analytical expressions for this bias, which depends on the residual difference between the model and real data. They can lead to biases not accounted for in previous calibration schemes. By measuring the model bias, noise bias and their interaction, we provide a complete statistical framework for measuring galaxy shapes with model fittingmethods from GRavitational lEnsing Accuracy Testing (GREAT)-like images. We demonstrate the noise and model interaction bias using a simple toy model, which indicates that this effect can potentially be significant. Using real galaxy images from the Cosmological Evolution Survey (COSMOS) we quantify the strength of the model bias, noise bias and their interaction. We find that the interaction term is often of a similar size to the model bias term, and is smaller than the requirements of current and near future galaxy surveys. © 2014 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society.