With the rise of distributed energy resources and the increasing activation of flexibility resources by Distribution Systems Operators (DSOs), the Transmission System Operators (TSOs) need to co-ordinate their actions with those of the DSOs. This research uses a look-ahead multi-interval (LA-MI) framework for analyzing this coordination and explores two formulations. Firstly in the exogenous DSO model, a mixedinteger linear program is developed to reflect the pragmatic approach in many real situations whereby the TSO can only anticipate statistically the actions of the DSO. In the embedded DSO model, as a comparator, we propose a new organizational setup for the TSO-DSO operational coordination mechanism. In the resulting bilevel decomposition, a new method to calculate Benders cuts is developed and tested on a modified IEEE 118-bus test system as a transmission network and two modified IEEE 33-bus test systems as distribution networks. The benefits of the LAMI coordination framework are substantial in comparison with the current Look-Ahead Single-Interval (LA-SI) coordination framework widely used in Europe.