The Total War series springs to mind: Shogun, Medieval, Rome, Medieval II, and some later ones depicting unapplicable time periods. Action on the strategic map is turn based (moving troops, diplomats, spies etc.; also building units and constructing buildings in towns), while combat takes place in real time. As the titles suggest, no fantasy content in these ones, and they're pretty detailed when it comes to period battle tactics.
If you want more fantasy and less history, and you don't insist on shiny graphics, there's Dominions 3, which is explicitly designed for multiplayer (though single player free-for-all can be played against the AI). Management is rather abstract yet complex, with spell research (hundreds of strategical and combat spells divided into a dozen schools and requiring different skill sets to cast), personnel management (cost/value ratio is very important, and your spellcaster units can become major combat factors if you properly manage their development and equipment) and the terrain dictating the production and placement of your troops. Dozens of factions vaguely based on historical cultures and various fantasy/literary tropes.
In combat, you don't get to control your armies. Instead, you give them standing orders about formations and basic battle plans (incl. what spells your casters should be casting), and they'll carry them out to the best of their abilities.