I am not the fan of multi-classing that I was when I started playing Dungeons & Dragons in the previous century, but some players are enamored of it and I feel an obligation to appease them rather than to proselytize. I'm just happy to find players willing to give older editions a chance. However, I am not willing to refrain from tinkering if it suits me. Lopsided level advancement for multi-class characters has never felt right to me, and on a purely practical level it's a nuisance. Gaining half-hit dice and half-bonuses are a consequence that I cannot abide. Moreover, there is no in-game excuse for such an arrangement. Unless experience is allocated to the class with which it was earned on a case by case basis (which is a level of bookkeeping in which I refuse to engage), then there are only two alternatives worth considering.
The first is what I call equal level advancement. This means that a multi-class character does not advance until enough experience has been earned to increase all of the character's classes by one level. In other words, instead of dividing earned experience amongst the character's classes (as is done in traditional lopsided level advancement), the experience costs of all of the classes are added together. When enough experience is earned, the character's level increases in all of his or her classes simultaneously. The multi-class character is recast as a single class with multiple facets. If it doesn't matter how the experience is earned, then this is the logical extension.
The second alternative is the OD&D (and Labyrinth Lord Original Edition Characters) method originally used for elves, but we could expand it to include any combination of classes and open it to any player character species. I'll call it separate level advancement. The multi-class combination must be declared when the character is created. [Edit: Or not. Why should it be? Perhaps a character initially plans to be single-classed, but has a change of heart or circumstances.] At the beginning of each adventure, the multi-class character decides which class to operate as, and all experience earned will be applied to that class only. Classes may be switched only between adventures. Characters may freely use the abilities of the class in which they are currently operating and any class in which they have previously gained one or more levels. If there is a difference in saving throws or attack rolls, the best one is used. Armor restrictions, however, remain in effect i.e. thiefly skills cannot be used when wearing armor heavier than leather, and magical spells cannot be cast when wearing non-elven armor.* Of course, the benefits of being multi-classed will not be felt at first level, but the rate of advancement in each class can be customized to taste. If one wanted to be a dabbler in magic at first level, and then lead the life of a swashbuckling thief forever after, that would be a viable option. Likewise, one could alternate as a fighter or a magic-user indefinitely.
This second alternative has the possibility of unbalancing the game, but I'd argue that multi-classing is inherently unbalanced. I'd rather do away with it, but I fear I'm in a minority.
In either equal or separate level advancement, I would take a cue from the Labyrinth Lord Advanced Edition Companion and allow nearly any class combination for any species (including human).
* Some say that magic-users cannot wear armor, but elves can. In truth, any spellcaster can wear elven armor, but no spellcaster (including elves) can wear non-elven armor. Elves just have a much easier time obtaining elven armor than non-elves do.