The ATMOSPHERE project is a 24-month European Union and Brazilian government-funded initiative to develop a framework and platform for trustworthy cloud services using a hybrid and federated international resource pool. The project aims to consider various dimensions of trustworthiness, such as security, privacy, and dependability, by developing mechanisms for a distributed telemedicine application to measure trustworthiness throughout the lifecycle. This will include a hybrid federated container platform, distributed trustworthy data management and processing services using Spark and privacy techniques, and network federation to enable secure multi-tenant resource migration.