A formal combat between two mounted knights armed with lances?

It was called a Tourney. The early tourneys were more of a battle rather than the jousts of later period, the aim of the tourney was to literally take people hostage and thus you would earn money off the ransom. Strangley the practise of a large battle diminished towards the end of the medieval era; but the peace talks between Henry VIII of England and the french king were held with a old style tourney which are still seen as Battle-honours for some of the older regiments of the british army.