We consider the hybridisation of the mu-calculus through the addition of nominals, binder and jump. Especially the use of the binder differentiates our approach from earlier hybridisations of the mu-calculus and also results in a more involved formal semantics. We then investigate the model checking problem and obtain ExpTime-completeness for the full logic and the same complexity as the modal mu-calculus for a fixed number of variables. We also show that this logic is invariant under hybrid bisimulation and use this result to show that - contrary to the non-hybrid case - the hybrid extension of the full branching time logic CTL* is not a fragment of the fully hybrid mu-calculus.