Network slicing is considered one of the key enabling technologies 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 coordinate and jointly slice their accessible spectrum resources in both licensed and unlicensed bands. For licensed band slicing, we propose an inter-operator spectrum aggregation method that 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. Because all MNOs enjoy equal rights to accessing these bands, we introduce the concept of right sharing for MNOs to share and trade their spectrum access rights. We develop a {\em modified back-of-the-envelope (mBoE) method} for MNOs to evaluate their {\em Value-of-Rights (VoR)} when coexisting with other wireless technologies. A {\em network slicing game} based on the overlapping coalition formation game is formulated to investigate cooperation between MNOs. We prove that our proposed game always has at least one stable slicing structure that maximizes the social welfare. To implement our proposed framework without requiring MNOs to reveal private information to other MNOs, we develop a distributed algorithm called D-ADMM-PVS. Performance evaluation of our proposed framework is provided using a discrete-event simulator that is driven by real MNO deployment scenarios based on 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 MNO in an urban setting.