Domain Name System (DNS) has become a backbone in internet and communications services which also plays a vital role in critical industrial systems (CIS) and Supervisory Control and Data Acquisition (SCADA) communication and transmission at large. Encapsulating DNS inside of HyperText Transfer Protocol Secure (HTTPS) as DNS over HTTPS (DoH) does not completely prevent intruders from exploiting access into the network. In this work, a hybrid deep learning model is proposed for efficient early detection and classification of network traffic into one of the following classes:- Non-DoH, benign-DOH, or malicious DoH. The proposed scheme incorporates the swiftness of the convolutional neural network (CNN) in extracting useful information and the ease of long short-term memory (LSTM) in learning long-term dependencies. The simulation results showed that the proposed scheme accurately classified traffics into the Non-DoH, Benign-DoH, and Malicious DoH classes. The accuracy, precision, training time, F1-Score, and recall rate are 97%, 96%, 41s, 96%, and 97%. Also, the proposed model had better computation time when compared to other contemporary algorithms.