IoT healthcare systems are interested in offering intelligent wearable devices, medical records, and biosensors, mainly designed by Internet of Things (IoT) devices. However, IoT healthcare systems suffer from various security threats and data privacy risks. The big challenge is to protect sensitive data in IoT healthcare systems against complex cyber-attacks. This study proposes a deep learning model with a zero-trust-enhanced cyber threat detection framework for protecting IoT healthcare systems. The proposed model, named DP-DL-ZT, employs differential privacy (DP) with integrated two deep learning (DL) models named convolution neural network (CNN) with long short-term memory (LSTM) for IoT healthcare systems. DP preserves user data privacy by adding noise to ensure data confidentiality. The two DL models are used to detect and classify the type of user and block the malware user. We integrated the CNN with LSTM to obtain high accuracy in the detection process because the CNN model is used to capture spatial features from input data and output to the LSTM model to capture temporal dependencies of input data. Integrated CNN + LSTM obtained high accuracy compared to using the single model in datasets in detection attacks. A zero-trust (ZT) function performs authentication and verification for benign users to gain access to IoT healthcare systems. The study is validated using ICU, CICIDS 2017, and WUSTL-EHMS-2020 datasets. The DP-DL-ZT model is compared with five deep learning models, such as LSTM, CNN, RNN, GRU, and FFN. The DP-DL-ZT model achieved the highest accuracy compared with other DL models.