Network slicing has been considered as a key enabling technology for 5G due to its ability to customize and "slice" a common resource to support diverse services and verticals. This paper introduces a novel inter-operator network slicing framework in which multiple mobile network operators (MNOs) can cooperate and jointly slice their accessible spectrum resources in both licensed and unlicensed bands. For the licensed band slicing, we propose the inter-operator spectrum aggregation method which allows two or more MNOs to cooperate and share their licensed bands to support a common set of service types. We then consider the sharing of unlicensed bands. Since all MNOs enjoy equal rights to access unlicensed bands, we introduce the concept of right sharing for MNOs to share and trade their spectrum access rights. We develop a modified back-of-the-envelop method for the MNOs to evaluate their value of rights when coexisting with other wireless technologies. We develop a network slicing game based on the overlapping coalition formation game to investigate the possible cooperation between MNOs. We prove that our proposed game always has at least one stable slicing structure that maximizes the social welfare. To evaluate the practical performance of our proposed framework, we develop a C++-based discrete-event simulator and simulate a possible implementation of our proposed framework over 400 base station locations deployed by two primary cellular operators in the city of Dublin. Numerical results show that our proposed framework can almost double the capacity for all supported services for each operator under certain conditions.