Integration between wireless sensor networks and traditional IP networks using the IPv6 and 6LoWPAN standards is a very active research and application area. A combination of hybrid network significantly increases the complexity of addressing connectivity and fault tolerance problems in a highly heterogeneous environment, including for example difierent packet sizes in difierent networks. In such challenging conditions, securing the communication between nodes with very diverse computational, memory and energy storage resources is at the same time an essential requirement and a very complex issue. In this paper we present an efficient and secure mutual authentication and key establishment protocol based on Elliptic Curve Cryptography (ECC) by which difierent classes of nodes, with very difierent capabilities, can authenticate each other and establish a secret key for secure communication. The analysis of the proposed scheme shows that it provides good network connectivity and resilience against some well known attacks.