If you've been following along with the recent posts I've done with new character classes for Basic/Expert D&D they were in part to fill in these gaps.
In B/X you have the Elf which is a Fighter/Magic-User, and Dwarves & Halflings which mix some Thief like abilities in with those of the Fighter. To this I've added the the Witch who is a kind of Cleric/Magic-User, and the Bard who is a mix of Magic-User and Thief. The Paladin & Anti-Paladin are Cleric/Fighters and finally the Monks & Assassins are Cleric/Thieves.
Each of the 4 main classes (Cleric, Fighter, Magic-User, Thief) can be combined with any of the other 3 by choosing one of the specialized classes.