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State-estimation plays a vital role to monitor, observe and understand the combined heat and electric network. In this paper, a hybrid framework is presented to accurately estimate the system states of electric distribution network and heat network, using the limited non-redundant measurements obtained from supervisory control and data acquisition and advanced metering infrastructure systems. The presented hybrid framework involves two steps, namely, the state-forecasting and the state-estimation. The state-forecasting uses a deep neural network to forecast the system states at every fifteen minutes interval, while these forecasted states are further used by the hybrid estimator, which uses a robust extended Kalman filter to estimate the system states with help of both datasets corresponding to supervisory control and data acquisition and advanced metering infrastructure systems, at hourly interval. The proposed framework does not completely rely on the system model at different instants. The effectiveness of the method is validated through thorough comparisons with simulation studies carried out using the Barry Island test system, United Kingdom. Satisfactory performance is observed even with the presence of bad data in the measurements.