Distributed generation by converter-interfaced renewable energy sources connected to distribution feeder nodes has been increasingly penetrating power grids, along with their expected contribution to frequency and voltage support services. This will change the perspective with which stability and dynamic behavior of power systems have been analyzed/simulated to date. Until a few years ago, only transmission systems were simulated in detail, while each distribution feeder was replaced by an aggregated load. This model reduction allows minimizing the CPU time of simulations and is deemed acceptable in the past. However, the ever-increasing share of distributed generation requires adopting accurate models of both transmission systems and active distribution feeders, which leads to a staggering increase in the total number of nodes/equations and CPU time. We propose a numerical method that is up to two orders of magnitude faster than existing methods in performing integrated transient stability simulations of transmission systems and distribution feeders in the three-phase frame. We show the numerical properties and efficiency of the proposed method by simulating a well-known transmission system connected to several distribution feeders with a high penetration of inverter-based resources.