The operation of drinking water supply networks is generally assessed using two complementary computer models. Firstly, the flow rates in the system are predicted from a hydraulic model with given input parameters and a network graph. Then the calculated pipe velocities are used in a transport reaction solver to determine various indicators for water quality, such as residence times, source tracings, and disinfectant concentrations. High parameter uncertainties require parameter estimations to be made to improve the predictions of the two coupled models. The objective of this paper is to assess if a dual calibration for these coupled models is possible through the use of a gradient method. Based on field data measurements, such as tank levels, pressures, flow rates and chlorine concentrations, a weighted least-squares problem is defined for an over-determined system to minimize the residuals between observed and model values. A direct solution based on the Levenberg-Marquardt method is proposed. The dual calibration was tested on two real networks and was shown to be effective even with inevitable unexpected circumstances. The parameter uncertainty, or even the observability, was found to be strongly linked to measuring device placement. Selecting measuring devices that are more sensitive may drastically improve the conditioning of the calibration problem.